# Numerical Simulation of Rock Mass Structure Effect on Tunnel Smooth Blasting Quality: A Case Study
## 2 Material and Methods
### Mathematical Model and Numerical Mode
#### 2.4.3 Numerical Model and Verification  
The finite element software LS-DYNA was used to establish the smooth blasting finite element model of the tunnel, whose rock mass structure was massive integrity structure, massive structure, layered structure, and cataclastic structure, by referring to the information of structural plane collected onsite, as shown in Figure 8. The dimension of the model along the X, Y, and Z directions was 80 m \(\times\) 80 m \(\times\) 60 m. The tunnel was 6.26 m high and 13.00 m wide. Except for the excavated part, the boundary surface of the model adopted the non-reflection boundary condition. The non-reflective boundary condition was defined by the keyword *BOUNDARY_NON_REFLECTING in LS-DYNA. The *CONTACT_SURFACE_TO_SURFACE command [30] in LS-DYNA was used to simulate the contact structural plane for the two adjacent blocks not to penetrate each other and to transmit normal pressure and tangential friction to each other. The properties of the structural plane were simulated by defining the normal and tangential stiffness of contact. Structural plane parameters referred to the formula of normal stiffness and tangential stiffness of rock mass structural plane proposed by [PERSON]:  
\[K_{n}\ =\ -7.15+1.75 JRC+2(JCS/JRC), \tag{3}\]  
\[K_{S}\ =\ 100/L\cdot JCS\cdot\tan\varphi_{r}, \tag{4}\]  
where, \(JRC\) is the roughness coefficient of the discontinuity, \(JCS\) is the compressive strength of the discontinuity, \(L\) is the trace length of the discontinuity, and \(\varphi_{r}\) is the friction angle of rock mass. According to the field measurement, \(JRC\) = 8, \(JCS\) = 27.34 MPa, \(L\) = 13 m, \(\varphi_{r}\) = 57\({}^{\circ}\) were put into the model correction inversion, and the normal stiffness and tangential stiffness of the structural plane in the model were 13.685 GPa and 5.474 MPa, respectively. In accordance with the actual situation of on-site blasting, the blast holes were arranged in the finite element model, the explosive center point was used as the detonation point, and the segmented micro-difference initiation technology was adopted. With reference to the actual situation of on-site blasting, blast holes were arranged in the finite element model. Taking the explosive center point as the initiation point, the piecewise millisecond initiation technology was adopted, and the initiation time difference of each hole in the model was set as 100 \(\upmu\)s. Among them, the cut hole was detonated at 0 \(\upmu\)s; the loosening hole was detonated at 100 \(\upmu\)s; the satellite hole and the heading hole were detonated at 200 and 300 \(\upmu\)s, respectively; and the peripheral hole was detonated at 400 \(\upmu\)s. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\rho\) (g/cm\({}^{3}\)) & \(v_{0}\) (cm/\(\upmu\)s) & \(PCJ\) (10\({}^{5}\) MPa) & \(A\) (10\({}^{5}\) MPa) & \(B\) & \(R_{1}\) & \(R_{2}\) & \(\omega\) & \(E_{0}\) (10\({}^{-1}\) J/cm\({}^{3}\)) \\ \hline
1.0 & 0.45 & 0.05 & 524.2 & 0.769 & 4.2 & 1.0 & 0.3 & 8.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material parameters of explosive model. Figure 8: Finite element model (unit: m). The total computation time was 1000 \(\upmu\)s. Solid 164 element was used for surrounding rock and explosives, and the numerical model created 2,504,199 nodes and 2,407,428 elements. The tunnel contours with different rock mass structures after blasting are shown in Figure 9. The influence of rock mass structure effect on tunnel smooth blasting quality was obvious. The numerical simulation of the four monitoring sections was compared with the on-site monitoring of the overbreak and underbreak of the tunnel face. Figure 10 shows the profile comparison of each section design, field monitoring, and numerical simulation. It can be seen that the design, field monitoring, and numerical simulation contours were similar in shape, and the overbreak and underbreak positions of the tunnel contour in numerical simulation and field monitoring were also relatively consistent.