# Formation Mechanism and Control Technology of an Excavation Damage Zone in Tunnel-Surrounding Rock
## 5 Finite Element Analysis and Removal of Stress Redistribution Factors  
Large finite element software FLAC3D has been widely used in geotechnical and underground engineering. It can be analyzed by the'mixed discrete method\" when simulating plastic failure. It can provide more accurate and reasonable results than the ordinary discrete integration method. Therefore, FLAC3D software was used for numerical simulation in this study. The tunnel excavation section area was approximately 150 m\({}^{2}\) with a span of 14.7 m and a height of 12.5 m. To avoid the influence of the model boundary effect, in the numerical model, the distance between the tunnel center axis and the left and right boundaries was greater than four times the tunnel span, the distance between the tunnel center axis and the upper and lower boundaries was also greater than three times the tunnel span. The excavation footage was 3 m. The whole calculation model was 120 m wide and 100 m high, with 49,152 units in total. The models are shown in Figures 12 and 13. Based on the physical and mechanical parameters of the surrounding rock, the final parameter values were as follows after trial calculation by referring to relevant manuals [29]: Elasticity modulus \(E=10\) GPa. Poisson's ratio \(u=0.3\). Frictional angle \(\varphi=35^{\circ}\). The cohesive force of the surrounding rock was \(1\times 10^{5}\) Pa. The tensile strength of the surrounding rock was \(3\times 10^{5}\) Pa. In the FLAC3D calculation, the rock mass deformation parameters were the volume modulus (\(K\)) and shear modulus (\(G\)). Therefore, the elastic modulus or deformation modulus (\(E\)) and Poisson's ratio (\(\mu\)) must be transformed into volume modulus (\(K\)) and shear modulus (\(G\)), and the transformation formula is as Equations (1) and (2). Figure 12: Plane view of finite element model. \[K=\frac{E}{3(1-2\mu)} \tag{1}\]  
\[G=\frac{E}{2(1+\mu)} \tag{2}\]  
The bulk modulus \(K\) and shear modulus \(G\) of the model can be calculated by Equations (3) and (4). Bulk modulus:  
\[K=\frac{E}{3(1-2\mu)}=8.33\times 10^{9}\ (\mathrm{Pa}) \tag{3}\]  
Shear modulus:  
\[G=\frac{E}{2(1+\mu)}=3.85\times 10^{9}\ (\mathrm{Pa}) \tag{4}\]  
In the FLAC3D dynamic calculation, four kinds of dynamic loads can be input: acceleration time history, velocity time history, displacement time history, and stress time history. The dynamic load input of this simulation adopted the monitored blasting vibration velocity time-history curve since the actual particle vibration velocity data were measured by field test. This effectively ensures that the numerical simulation calculations are as consistent as possible with the field blasting tests. The monitored vibration velocity in Figures 3 and 5 was transformed into the vibration velocity time-history curve required by FLAC3D, as shown in Figures 14 and 15. Figure 14: Data after nonelectric detonator vibration test and transition. Figure 13: Three-dimensional view of finite element model. In order to combine the field tests, the numerical simulation is carried out according to the actual blasting footage of 3 m. The nonelectric detonator test caused 137.33 m\({}^{3}\) surrounding rock unit failure in the footage through the statistical data in Table 4, and the average thickness of the surrounding-rock loose circle is shown in Table 5. The average damage depth of the entire excavation section caused by explosive initiation can be obtained by dividing the surface area of the excavation profile within the footage length. The average failure depth of surrounding rock damage caused by the nonelectric detonator test is close to 2 m. This is basically consistent with the results monitored in the field test, which verifies the correctness of the numerical model. Similarly, 104.86 m\({}^{3}\) surrounding rock units failed in the electronic detonator results, and the average failure depth was 1.514 m. The calculated average depth of electronic detonators is obviously smaller than that of nonelectric detonators.