5.2. The Effects on the Pressure-Time Curves of Shock Wave above Different Grounds
Figure 7,
Figure 8,
Figure 9 and
Figure 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
Figure 8,
Figure 9 and
Figure 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.
It can be seen from
Figure 8,
Figure 9 and
Figure 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°, which has nothing to do with the property of the ground.
5.3. The Effects on the Peak Overpressure of Shock Wave above Different Grounds
As shown in
Figure 11a, the peak overpressure curves of gauges at 2 m height for different grounds present different rules with
x. For rigid ground, when
x is not greater than 50 m, the peak overpressure of the shock wave is larger than that of others. However, when
x is greater than 50 m, the peak overpressure gradually approaches that of the concrete ground and soil ground. This is due to the fact that the rigid ground does not absorb energy of the shock wave, but reflects the shock wave and generates regular and irregular reflections with the incident waves, enhancing the shock wave. The enhancement effect is more obvious when
x is smaller, and less when
x increases. For the explosion above concrete ground and soil ground, when
x is not greater than 10 m, the peak overpressure of shock wave is very close to that in the air. However, when
x is greater than 10m and less than 40 m, peak overpressure starts to be higher than that in the air, and gradually approaches to the peak overpressure of rigid ground as
x increases. When
x is greater than 40 m, the peak overpressures of the shock wave above different grounds gradually approach, but all of them are higher than the peak overpressure of explosion in the air.
Figure 11b presents the peak overpressure curves of gauges at 4 m height. For rigid ground, when
x is not greater than 70 m, the peak overpressure is higher than that of others. However, when
x is greater than 70 m, the peak overpressure is gradually close to that of concrete and soil ground. For concrete and soil ground, when
x is not greater than 20 m, the peak overpressure of shock wave is very close to that in the air. However, when
x is greater than 20 m and less than 60 m, peak overpressure starts to be higher than that in the air, and gradually approaches to that of rigid ground. When
x is greater than 60 m, the peak overpressures of the shock wave above different grounds gradually approach.
Figure 11c presents the peak overpressure curves of gauges at 6 m height. For rigid ground, when
x is not greater than 20 m, the peak overpressure of the shock wave above different grounds tends to be consistent. However, when
x is greater than 20 m and not greater than 100 m, the peak overpressure is higher than that of concrete ground and soil ground. When
x is greater than 100 m, the peak overpressure is gradually close to that of concrete ground and soil ground. For concrete ground and soil ground, when
x is not greater than 30 m, the peak overpressure of the shock wave is very close to that in the air. However, when
x is more than 30 m, peak overpressure starts to be higher than that in the air, and gradually approaches to the peak overpressure of rigid ground as
x increases.
Figure 11d presents the peak overpressure curves of gauges at 8 m height. For rigid ground, when
x is not greater than 30 m, the peak overpressure of the shock wave above different grounds tends to be consistent. However, when
x is greater than 30 m, the peak overpressure is higher than that of concrete ground and soil ground. For concrete ground and soil ground, when
x is not greater than 30 m, the peak overpressure of the shock wave is very close to that in the air. However, when
x is greater than 30 m, peak overpressure starts to be higher than that in the air, but is lower than that above the rigid ground. As for
Figure 11e, the law of peak overpressure curves is generally similar to that in
Figure 11d, except for the value of the peak overpressure.
From what has been discussed above, when h is not greater than 4 m, the peak overpressure generated by the explosion above the rigid ground is higher when x is relatively small, and the enhancement effect on the overpressure is no longer obvious with the increase of x. When x is small, the peak overpressure of concrete ground and soil ground is the same as that in the air. However, when x increases to a certain extent (10 m or 20 m), the enhancement effect on the shock wave gradually becomes prominent, which is consistent with that of rigid ground. As for h greater than 4m and less than 10 m, the peak overpressure curves of different grounds are the same when x is small, while the differentiation begins when x reaches a certain value. The peak overpressure of rigid ground is higher than that of concrete and soil ground, and the peak overpressure of concrete and soil ground is higher than that of the air. This is mainly because when x is relatively small, the incident wave plays the main role, while when x is relatively big, it is the superimposed Mach wave that plays a major role.
5.4. The Peak Overpressure Factor of Different Ground
It is assumed that the peak overpressure of gauges in Model 1 to Model 3 is Pground, and the peak overpressure of gauge in Model 4 is Pair, then “peak overpressure factor” is defined in this paper, which is α = Pground/Pair. It reflects the enhancement effect for peak overpressure of different grounds.
As shown in
Figure 12a, for rigid ground, when
x is small,
α at different heights varies greatly. The lower the height, the greater the
α is, and the maximum reaches 3.8. With the increase of
x,
α of different heights gradually approaches, and eventually approaches 2. As shown in
Figure 12b,c, for the concrete and soil ground, with the increase of height,
α increases successively from 1, the lower the height, the greater the rise will be, and then starts to stabilize at a specific value. The maximum
α with a height of 6 m is 2.1, and the minimum
α with a height of 10 m is 1.43.
It can be seen from
Figure 12a–c that, for rigid ground, the enhancement effect of peak overpressure with different height is roughly the same, and the peak overpressure factor is about 2. However, the concrete ground and soil ground have different effects on the peak overpressure factors at different heights. Among them, peak overpressure factor of 6m height is the largest, reaching 2.1, while the factor of 10 m height is the smallest, which is 1.43.