# Investigation of Rock Joint and Fracture Influence on Delayed Blasting Performance
## 5 Analysis of Blasting Simulation
The JWL equation is used to describe the emulsion explosives state, which was expressed as  
\[P=A(1-\frac{w}{R_{1}V})\mathrm{e}^{-R_{1}V}+B(1-\frac{w}{R_{2}V})\mathrm{e}^{- R_{2}V}+\frac{w}{V}E, \tag{15}\]  
where \(P\) is the required pressure value; \(E\) is the internal energy of the detonation product per unit volume; \(V\) is the volume of the detonation product; \(A\), \(B\), \(R_{1}\), \(R_{2}\), and \(w\) are empirical parameters; and the explosives are selected according to the site conditions. The parameters are detailed in Table 3.  
When defining the boundary conditions, define the top, slope, and foot surface of the step as free surfaces; that is, displacement can be generated, and stress waves in the rock mass can be reflected. All remaining surfaces are set to non-reflective boundary conditions; that is, there is no change in displacement and no reflection of stress waves. The underside is set as a perspective surface, which allows the energy of detonation to be released. Numerical simulation software is used to obtain the dynamic distribution of effective stress within the surrounding rock mass after the explosion. According to the statistics of the mechanical test results, the average tensile strength is 5 MPa, and the value is used as the critical value to judge whether the rock can yield. The rock mass in the stress area is analyzed in a critical state or plastic state by the color change in the effective stress cloud. The effective stress is greater than the tensile strength; otherwise, it does not occur. The material parameters are restored and set with reference to the physical and mechanical parameters in the field; boundary load constraints are imposed. By calibrating against the field conditions, a reasonable time step, CPU speed, and storage space are obtained. Then, the symmetry axis is used as a constraint, and transmission boundaries and reflection boundaries are imposed. Figure 4 shows a typical setup. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Density** & **Young’s Modulus** & **Poisson’s Ratio** & **Tensile** & **Compressive** \\
**(g/cm3)** & **(\(\times 10^{4}\) MPa)** & **Strength (MPa)** & **Strength (MPa)** \\ \hline
2.43 & 5 & 0.26 & 5 & 130 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Rock properties within highwall bench. Figure 4: Blasting model of micro-delayed holes. A—Stemming 7 m, B—Explosive 6 m, C—Interval 5 m, D—Explosive 8 m, E—Joint. Upon the completion of the calibration, changes in the Mises stress nephogram of highwall bench blasting at different times are obtained. In Figure 5, the charge column at the lower part of the blast hole detonates first, and the detonation wave propagates from the bottom to the top of the hole. When \(t=1197\) us, the shock wave generated by the explosive induces a fracture in the surrounding rock, and the stress wave of the charge column begins to propagate to the hole. In comparison, the stress wave that propagates to the bottom of the hole is pear-like and propagates downward. When \(t=1498\) us, blasting spreads radially from the hole center like water ripples. At the same time, the value gradually decreases. Stress in the crushing area around the blasthole is relatively concentrated, and the wave propagating to the crack area can pass through the depth of color in the figure. The change is then analyzed, and the color of the outer layer is weakened to a certain extent from the blast hole. With the propagation of the detonation wave in the hole, the detonation wave attenuates into a stress wave, and rock mass hinders the propagation of the shock wave. This is similar to the propagation of ocean waves to the position of the free surface layer by layer. The intensity of the shock wave is lower than the damage strength of the rock, and the sub-layer shock wave supplements the shock wave energy that is not enough to break the rock. This further pushes the explosive gas into the crack, forming a gas wedge effect, which further deepens and expands the crack.