## 5 Results and Analysis
### The Effects on the Pressure-Time Curves of Shock Wave above Different Grounds  
Figures 7-10 respectively show the pressure-time curves of the shock wave of gauges A1 to A12 when the explosion occurs above different grounds. As shown in Figure 7, shock wave pressure of different gauges rises linearly and then decreases gradually with time. The pressure curve shows the single-peak characteristic, and the peak overpressure decreases gradually with the increase of \(x\). This is mainly because the scaled distance to explosion center increases from A1 to A12. Different from the explosion pressure curves explosion in the air, the gauges in Figures 8-10 are divided into two groups according to the characteristics of the pressure-time curves. Group 1 is the gauges from A1 to A4, while Group 2 is the gauges from A5 to A12. The pressure-time curves of the two groups show different characteristics. The pressure-time curves in Group 1 have obvious bimodal characteristics. The first peak is the incident wave, and the second one is the reflected wave. As is shown in Figure 8, the smaller the \(x\) is, the higher reflected peak overpressure is. For gauges A1 and A2, the peak pressure of the reflected shock wave is larger than that of the incident one, while the result is opposite for gauges A3 and A4. This is mainly because the smaller \(x\) is, the smaller the incident angle is, and the higher the energy of the reflected shock wave will be. The pressure-time curves in Group 2 show a single peak characteristic. This is because the Mach reflection is formed at this zone, and the peak overpressure is the maximum pressure of the composite wave. As can be seen, the peak pressure of the gauge at the same position is higher than that in the air. As is shown in Figure 9, for gauges A1 and A2, the bimodal characteristics of the pressure-time curves are not obvious. While for gauges A3 and A4, and the pressure-time curves, have obvious bimodal characteristics. The peak pressure of incident wave and reflected wave is relatively close, but obviously lower than the peak pressure of rigid ground. This is mainly because when the incident angle is small, more energy is sent into the ground, so the reflected wave is not obvious. However, with the increase of the incident angle, the energy sent into the ground by the shock wave decreases, so the reflected wave is obvious. The pressure-time curves in Group 2 show a single peak characteristic like the curves in Figure 8b, but there is just a decrease in the overpressure at the gauge. The curve in Figure 10 shows a similar pattern to that in Figure 9, except that there are some differences in the pressure values.  
Figure 7: Pressure-time curves at 2 m gauges of shock wave in the air.  
It can be seen from Figures 8-10 that, the pressure curves of gauges from A1 to A4 have two peaks. The first one is the peak pressure of the incident wave, and the second one is the peak pressure of the shock wave reflected by the ground. However, for gauges from A5 to A12, this phenomenon is not obvious. Only one obvious peak pressure appears, indicating that Mach reflection occurs. Therefore, for the shock wave generated by the explosion above the ground, Mach reflection starts to occur at the incident angle of about 40\({}^{\circ}\), which has nothing to do with the property of the ground.  
Figure 8: Pressure-time curves at 2 m gauges of shockwave above the rigid ground.  
Figure 10: Pressure-time curves at 2 m gauges of shock wave above the soil ground.  
Figure 9: Pressure time curves at 2 m gauges of shock wave above the concrete ground.