# Blasting Vibration Control and Signal Analysis of Adjacent Existing Deterioration Tunnels
## 3 Numerical Simulation of Blasting Vibration Control
### Model Overview  
According to the actual engineering background, ANSYS/LS-DYNA was used to establish the geometric model, as shown in Figure 3a. The overall model size is 60 \(\times\) 20 \(\times\) 40 m, and the blasting hole is located in the center of the new tunnel. It is 15 m away from the surrounding rock on the right side of the existing tunnel. The three groups of blasting holes are arranged successively from inside to outside to simulate tunnel blasting holes. The schematic diagram of blasting holes is shown in Figure 3b. The mechanical cutting method means that the center blasting hole changed into air material, and the cutting diagram is shown in Figure 3c. The model unit adopts an 8-node SOLID164 solid unit as well as Lagrange grid division. The model grid is shown in Figure 3d. The model is divided into 411,272 elements. A total of 5 parts were created in this numerical simulation modeling process. Part 1 simulates the tunnel surrounding the rock. Part 2 simulates the fluid-structure coupling part. Part 3 simulates the explosive portion of the center blasting hole. Part 4 simulates the explosive portion of the auxiliary hole. Part 5 simulates the explosive portion of the peripheral hole. The numerical simulation of the blasting process adjacent to the existing tunnel involves rock and explosives. An arbitrary Lagrange-Euler algor  
Figure 3: Model diagram. (**a**) Global model; (**b**) blasting hole; (**c**) mechanical cutting model; (**d**) the model grid. simulation, that is, fluid-structure coupling algorithm. The explosive material is the No. 8 detonator, and the material keyword added when modifying the k file separately is *MAT_HIGH_EXPLOSIVE_BURN. The constitutive model of explosive adopts the JWL equation of state, and the relation is as follows:  
\[p=A(1-\frac{\omega}{R_{1}V})e^{-R_{1}V}+B(1-\frac{\omega}{R_{2}V})e^{-R_{2}V}+ \frac{\omega E_{0}}{V} \tag{1}\]  
\(P\) is the detonation pressure, Mpa; \(V\) is the volume; \(E_{0}\) is the internal energy of the initial volume; and \(A\), \(B\), \(R_{1}\), and \(R_{2}\) are material constant. The keyword of the equation of state after the explosive explosion is *EOS_JWJ and the specific parameter settings are shown in Table 2.  
The HJC constitutive model is a rate-dependent constitutive model proposed by [PERSON] et al. to solve the problem of large deformation under high strain rates and high pressure loads. The model consists of a yield strength function, state equation, and damage evolution equation. At present, it is widely used in the dynamic impact failure process of rock materials [21]. The yield strength model is standardized by equivalent stress:  
\[\sigma^{*}=[A(1-D)+BP\times N](1+C\ln\varepsilon_{*}) \tag{2}\]  
\[\sigma^{*}=\sigma/f_{c} \tag{3}\]  
\[P^{*}=P/f_{c} \tag{4}\]  
\[\varepsilon^{*}=\varepsilon^{\prime}/\varepsilon_{0} \tag{5}\]  
\(\sigma\) is actual equivalent stress; \(f_{c}^{*}\) is quasi-static uniaxial compressive strength; \(P^{*}\) is standardized hydrostatic pressure; \(P\) is actual hydrostatic pressure; \(\varepsilon^{*}\) is dimensionless strain rate; \(\varepsilon\) is true strain rate; and \(\varepsilon_{0}\) is reference strain rate. D is the degree of damage (\(0\leq D\leq 1.0\)). \(A\), \(B\), \(C\), and \(N\) are the strength parameters of the material. The H-J-C material model in ANSYS/LS-DYNA is selected for rock materials. The specific material properties are defined by the keyword *MAT_JOHNSON_HOLMQUIST_CON CRETE, and the specific parameters are shown in Table 3.  
In Table 3, MID is the material ID; \(p_{0}\) is the density, g/cm\({}^{3}\); G is the shear modulus; and A, B, N, C, and SFM are the strength parameters. Fc is the static yield strength. T is the tensile strength; EPS is the reference strain rate; EFM is the minimum fracture strain. Pc is the volume stress; UC is the volume strain; PL is the material limit volume stress; UL is the material limit volume strain; D\({}_{1}\) and D\({}_{2}\) are damage constants; and K\({}_{1}\), K\({}_{2}\), and K\({}_{3}\) are pressure constants. F