## 3 Rock Breaking Design Program
### Dynamic Blasting
#### 3.1.2 Monitoring and Fitting
Actual geotechnical media are discontinuous and inhomogeneous, and it is currently almost impossible to describe these envelopes mathematically directly and objectively. The rock mass is usually regarded as a homogeneous and continuous elastic medium. In this paper, ANSYS 16.0 is used to simplify the model, that is, rock and soil are regarded as elastic-plastic materials. The material of the model is chosen to simulate the geotechnical medium, and the yield condition is shown in Equation (9). The constitutive relationship and numerical model are presented in Figure 8. The concrete of roadbed is simulated by the material of the model. According to the data provided by the geological report and indoor test, the main parameters of the selected material of the model are illustrated in Tables 4 and 5. \[\varphi=\frac{1}{2}\xi_{ij}^{2}-\frac{\sigma_{y}^{2}}{3}=0 \tag{9}\]  
\[\xi_{ij}=s_{ij}-a_{ij},\ \sigma_{y}=\left[1+\bigg{(}\frac{\dot{\varepsilon}}{C} \bigg{)}^{\frac{1}{p}}\right](\sigma_{0}+\beta E_{p}\varepsilon_{eff}^{p}).\]  
where \(s_{ij}\) is the Cauchy stress tensor; \(p\) and \(C\) are input constants; \(\sigma_{0}\), \(\beta\) are the initial yield stress and hardening parameter, respectively; \(\dot{\varepsilon}\) is the strain rate, \(\dot{\varepsilon}=\sqrt{\dot{\varepsilon}_{ij}\dot{\varepsilon}_{ij}}\); \(E_{p}\) is the plastic hardening modulus, \(E_{p}=\frac{E_{p}E}{E-E_{p}}\), with \(E\) being the elastic modulus, \(E_{t}\) being the tangential modulus; and \(\varepsilon_{eff}^{p}\) is the effective plastic strain. In general, the ramp-up time of the blast load is 8-12 ms, and the unloading time is 80-100 ms. To better analyze the propagation law of the blasting vibration seismic wave in the modeled medium, the computation time of the dynamite explosion simulation in this study is set to 0.3 s and the blast vibration seismic wave propagates in the modeled medium. (1) Analysis of blasting Vibration Velocity  
The maximum vibration velocity nephograms of the highway roadbed in each direction during blasting under three working conditions are extracted, as presented in Figure 9. Figure 10 presents the maximum vibration velocities of the highway roadbed, underground  
Figure 8: Numerical model and constitutive relationship. pipeline, and high-speed rail line under each condition, where they are compared with the fitted values. It can be seen from Figure 9 that the maximum vibration velocities of the highway roadbed under the three conditions are all located at the nearest point on the side of the head-on blast, and their values are within the specified range. It can be seen from Figure 10 that the simulated and the calculated values of vibration velocity under the three conditions are similar, indicating that the numerical simulation results are credible, and confirming the feasibility of applying the parameters in the empirical formula of [PERSON] to the proposed tunnel project. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **\(\mathbf{\beta}\) (g/cm\({}^{3}\))** & **D (cm/\(\mathbf{\mu}\)s)** & **P (MPa)** & **A (MPa)** & **B (MPa)** \\ \hline Value & 1.2 & 0.48 & 0.097 & 2.144 & 1.82 \(\times\) 10\({}^{-3}\) \\ \hline
**Parameters** & **R\({}_{1}\)** & **R\({}_{2}\)** & **\(\mathbf{\omega}\)** & **E\({}_{0}\) (J/cm\({}^{3}\))** & **V\({}_{0}\)** \\ \hline Value & 4.2 & 0.9 & 0.15 & 3.60 \(\times\) 10\({}^{3}\) & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main parameters of numerically simulated explosives.