# Numerical Simulation of Rock Mass Structure Effect on Tunnel Smooth Blasting Quality: A Case Study
## 2 Material and Methods
### Orthogonal Numerical Test Design of Rock Mass Structure Effect  
In smooth blasting, many factors affect the overbreak and underbreak of the tunnel, mainly including those related to blast hole layout scheme and rock mass structure, such as peripheral hole spacing, heading hole spacing, the vertical distance between heading hole and peripheral hole, rock mass density, compressive strength, other physical and mechanical parameters, and structural plane distribution. All have varying degrees of influence on the blasting effect. If the influence of various factors on the overbreak and underbreak of tunnel smooth blasting was studied through comprehensive numerical tests, the number could be huge. Orthogonal test design is a test design method that uses the orthogonal table to arrange and analyze multifactor tests. It is an efficient test design method to study the influence of multi factors and multi levels through the orthogonal table. It also uses some tests to replace all tests to reflect the overall situation. Therefore, in this study, an orthogonal numerical test scheme was designed to comprehensively analyze the influencing factors of the overbreak and underbreak of smooth blasting in tunnels with different rock mass structures. Due to the differences in the influencing factors of overbreak and underbreak of tunnel smooth blasting in different rock mass structures, different influencing factors were considered for different rock mass structures. The orthogonal numerical test factors of the massive integrity structure, massive structure, layered structure, and cataclastic structure rock mass are shown in Tables 4-7. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Rock Structure Type**} & \multicolumn{3}{c}{**Area (m\({}^{2}\))**} \\ \cline{2-4}  & **Field Monitoring** & **Numerical Simulation** & **Different** \\ \hline Massive integrity structure & 65.81 & 65.94 & 0.19\% \\ Massive structure & 66.45 & 66.59 & 0.21\% \\ Layered structure & 66.95 & 66.85 & 0.15\% \\ Cataclastic structure & 71.51 & 71.63 & 0.17\% \\ \hline \end{tabular}
\end{table} 
Table 3: Tunnel smooth blasting section area of numerical simulation and field monitoring. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{6}{c}{**Factors**} \\ \cline{2-7}  & \(\boldsymbol{\gamma\) (\({}^{\circ}\))} & \(\boldsymbol{\alpha\) (\({}^{\circ}\))} & \(\boldsymbol{D\) (\(\boldsymbol{m}\))} & \(\boldsymbol{P\) (\(\boldsymbol{cm}\))} & \(\boldsymbol{H\) (\(\boldsymbol{cm}\))} & \(\boldsymbol{S\) (\(\boldsymbol{cm}\))} \\ \hline
1 & 0 & 0 & 1.0 & 40 & 90 & 40 \\
2 & 20 & 20 & 1.25 & 50 & 100 & 50 \\
3 & 40 & 40 & 1.5 & 60 & 110 & 60 \\
4 & 60 & 60 & 1.75 & 70 & 120 & 70 \\
5 & 80 & 80 & 1.8 & 80 & 130 & 80 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The influencing factors and level of the layered structure rock mass. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{6}{c}{**Factors**} \\ \cline{2-7}  & \(\boldsymbol{\gamma\) (\({}^{\circ}\))} & \(\boldsymbol{\alpha\) (\({}^{\circ}\))} & \(\boldsymbol{D\) (\(\boldsymbol{m}\))} & \(\boldsymbol{P\) (\(\boldsymbol{cm}\))} & \(\boldsymbol{H\) (\(\boldsymbol{cm}\))} & \(\boldsymbol{S\) (\(\boldsymbol{cm}\))} \\ \hline
1 & 1.5 & 50 & 0.2 & 40 & 90 & 40 \\
2 & 1.8 & 70 & 0.4 & 50 & 100 & 50 \\
3 & 2.1 & 90 & 0.6 & 60 & 110 & 60 \\
4 & 2.4 & 110 & 0.8 & 70 & 120 & 70 \\
5 & 2.7 & 130 & 1.0 & 80 & 130 & 80 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The influencing factors and level of the cataclastic structure rock mass.