# The Preparation of Active Support-Based Sealing Material and Sealing Effect Analysis
## 4 Engineering Application
### Theoretical Analysis of Borehole Areas under Active Support Force  
According to the concept that the gas drainage borehole is taken as a miniature round roadway, when the borehole is excavated, a broken ring plastic zone would be formed around the borehole. In other words, a fissure field is formed, as shown in Figure 12. The radius of the plastic zone around the borehole and that of the breakage zone can be calculated using Equations (2)-(4) [21].  
\[R_{p}=R_{0}\bigg{[}\frac{(p_{0}+c\cot\varphi)(1-\sin\varphi)}{(p_{1}+c\cot \varphi)}\bigg{]}^{\frac{1-\sin\varphi}{2\sin\varphi}}, \tag{3}\]  
\[R_{s}=R_{0}\bigg{[}\frac{(p_{0}+c\cot\varphi)(1-\sin\varphi)}{(1+\sin\varphi)( p_{1}+c\cot\varphi)}\bigg{]}^{\frac{1-\sin\varphi}{2\sin\varphi}}, \tag{4}\]  
Figure 11: Stratigraphic columns.  
Figure 10: The active support force–time curve of sealing materials with different expansion rates.  
\[\mu=\frac{R_{0}\sin\varphi}{2G}\frac{(p_{0}+c\cot\varphi)^{\frac{1}{\sin\varphi}}(1- \sin\varphi)^{\frac{1-\sin\varphi}{2\sin\varphi}}}{(p_{1}+c\cot\varphi)^{\frac{1 -\sin\varphi}{2\sin\varphi}}}, \tag{5}\]  
The 2404 belt bottom drainage roadway adopts the method of drilling through strata. The borehole passes through mudstone and siltstone. Via the coring test of the borehole rock, its mechanical parameters are obtained and shown in Table 4. The burial depth of the 2404 belt bottom drainage roadway is 700 m, its ground stress is 17.5 MPa and the diameter of the borehole is 94 mm. The radius of the plastic zone of the borehole, that of the borehole breakage zone, and the displacement around the borehole can be calculated in two scenarios: with or without active support force. The calculation results are shown in Table 5.  
As can be determined from Table 5, with the increase in the active support force provided by the sealing material, the radius of the plastic zone and breakage zone decreases  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rock** & **Internal Friction Angle \(\varphi\)** & **Cohesion c** & **Shear Modulus/MPa** \\ \hline mudstone & 30 & 1.20 & 347.2 \\ siltstone & 36 & 2.75 & 812.5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The mechanical parameters of mudstone and siltstone.  
Figure 12: Stress distribution map of round borehole surrounding rock. I—breadage zone; II—plastic zone; III—elastic zone; IV—in situ stress zone.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Rock**} & **Borehole** & **Active** & **Plastic Zone** & **Broken Zone** & **Surrounding** \\  & **Radius/mm** & **Support** & **Radius/mm** & **Radius/mm** & **Displace-** \\  & & **Force/MPa** & **Total** & **Total** & **Total** \\ \hline \multirow{4}{*}{mudstone} & \multirow{4}{*}{99} & 2.63 & \(135.5\) & 99.7 & 16.9 \\  & & 2.10 & 143.9 & 104.2 & 17.9 \\  & & 1.40 & 157.7 & 111.2 & 19.6 \\  & & 0 & 204.0 & 130.8 & 25.5 \\  & & 2.63 & 104.9 & 89.2 & 4.0 \\ \multirow{2}{*}{siltstone} & \multirow{2}{*}{99} & 2.10 & 108.1 & 91.9 & 4.1 \\  & & 1.40 & 113.1 & 96.1 & 4.3 \\  & & 0 & 126.3 & 107.4 & 4.8 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The radius of the plastic zone and breakage zone, and the displacement around the borehole.  
accordingly; the displacement around the borehole also displays a similar changing trend. This indicates that the active support force of the sealed borehole can effectively inhibit the development of cracks around the hole and reduce the generation of a gas leakage channel. At the same time, the mechanical properties of the borehole rock also have a great influence on the development of a borehole fissure. Under the action of the same burial depth and active support force, the larger the mechanical parameters of the rock are, the smaller the radius of the plastic zone and the breakage zone is, and the smaller the displacement around the borehole is.