# Research on Seismic Wave Quality Factor of Marble Jointed Rock Mass under SHPB Impact
## 5 Numerical Simulation of Damage and Fracture of Rock Mass under Explosive Dynamic Loading
### Selection of Numerical Models for Materials and Explosives
#### 5.2.4 The Failure Model
The state equation of the model is linear, the strength model is linear elastic, and the failure model is linear tensile fracture softening damage model of maximum principal stress. The state equation of explosive is \(JWL\) state equation, the strength model is None, and the failure model of explosive is None. Figure 11: Diagram of softening model \(\sigma_{1}-\varepsilon_{F}\). The simulated size diameter of the model is 50 mm, the aperture radius is 2 mm, and the cartridge radius is 1.2 mm. Because engineering rock mass is infinite rock mass, when the explosion shock wave generated after explosive explosion propagates in rock mass it will gradually attenuate to stress wave, and finally attenuate to sound wave and dissipate, without wave reflection. The model adopts Transmit boundary condition, and when the explosion stress wave propagates to the boundary it will spread out and will not form reflected tension wave at the boundary. Therefore, Transmit boundary conditions can better simulate the propagation characteristics of stress wave in rock mass explosion. Figure 12a-f shows the process from the moment of detonation of the explosive near the hole to the propagation of explosive shock wave. The seismic wave quality factor of rock mass is the ratio of the maximum variable performance to the dissipated energy when the seismic wave propagates in the rock mass, and it is a dimensionless parameter. The AUTODYN-Code is used to carry out numerical simulation, and the rock mass is used as a porous medium. By setting the numerical model rock mass porosity, the damage and fracture state of the rock mass with different quality factors under the dynamic load of explosion can be simulated by weakening the parameters, as shown in Table 2. Adjust the porosity of the rock mass to simulate the damage and fracture characteristics of the rock mass with different quality factor models under dynamic explosion loading, as shown in Figure 13. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Porosity/\%**} & **Model** & **Hole Ra-** & **Radius of** & **Equation** & **Strength** & **Failure** \\  & **Size/mm** & **dius/mm** & **Cartridge/mm** & **of State** & **Model** & **Model** \\ \hline
0.1 & 25 & 2 & 1.2 & _JWL_ & None & None \\
0.15 & 25 & 2 & 1.2 & _JWL_ & None & None \\
0.18 & 25 & 2 & 1.2 & _JWL_ & None & None \\
0.25 & 25 & 2 & 1.2 & _JWL_ & None & None \\ \hline \end{tabular}
\end{table} 
Table 2: Different porosity numerical simulation parameters. Figure 12: Effect diagram of stress wave propagation after detonation. Figure 13 shows that the fracture range of the rock mass increases gradually with the increase in the rock mass porosity under the same explosive dynamic load conditions. The rock mass near the blasthole presents a compression-shear crushing zone under the ultra-high loading rate of the shock wave. The four fracture renderings show that the radius of the compression-shear damage zone increases gradually with the increase in porosity, but it is not obvious. The porous media properties of rock mass cause the energy of the blast shock wave to decay exponentially in the range of three to seven times the coil, and then decay into a stress wave. Under the action of attenuated stress wave, the fractures of the surrounding rock mass show tensile fracture characteristics, and no shear fracture cracks appear. When the energy release rate of the stress wave at the tip of the dynamic expanding crack is less than the energy dissipation rate required for the crack expansion, the dynamic expanding crack will stop expanding. Figure 13: Damage and fracture characteristics of rock mass with different porosity under explosive dynamic load. (**a**) The porosity is 0.1%; (**b**) The porosity is 0.15%; (**c**) The porosity is 0.18%; (**d**) The porosity is 0.25%.