Experimental Study on Blasting Energy Distribution and Utilization E ﬃ ciency Using Water Jet Test

: The blasting stress wave and blasting gas generated by explosive blasting are the two main motive powers of rock fragmentation. An experimental method based on water jet test is used to study the energy distribution ratio of blasting stress wave and blasting gas; the utilization e ﬃ ciency of blasting energy under di ﬀ erent borehole constraint conditions is also analyzed. It proves that the blasting stress wave does not cause the water jet, and the blasting gas is the only power of the water column jet. The results show that the energy of the blasting gas and blasting stress wave respectively account for about 64% and 36% of the total energy generated by the explosion of lead azide. The utilization e ﬃ ciency of the blasting gas energy under strong, medium, and weak constraint conditions is 100%, 80%, and 52%, respectively. The borehole constraint condition is crucial for the e ﬀ ective utilization of blasting energy.


Introduction
Explosive blasting is an extremely rapid chemical energy release process that has a strong impact on the surrounding medium and produces a large amount of blasting gas [1]. In the rock blasting field (e.g., roadway excavation [2,3] and ore fragmentation [4]), the effective utilization of blasting energy and the efficient fragmentation of rock are currently the subject of a great deal of research. At present, the theory of the combined action of blasting stress wave and blasting gas [5] is more practical and accepted by most researchers because it comprehensively considers the role of blasting stress wave and blasting gas in the rock failure process. Based on this theoretical consensus, it is hoped that the energy distribution characteristics of the blasting stress wave and blasting gas and the effects on rock fragmentation can be quantitatively analyzed in order to enrich rock blasting theory. Many scholars have used some feasible methods to study this [6][7][8][9], which has played a positive role in the understanding and development of rock blasting theory.
In the study of the action effect of blasting stress waves, Banadaki et al. [9] shielded the effect of blasting gas on the rock by inserting a copper tube into the borehole, and combined experimental results with numerical simulation to study the effect of the blasting stress wave on rock damage. Yang et al. [1,10] used two-dimensional model experiments with the borehole open to shield the effect of blasting gas, and studied the effects of the blasting stress wave and blasting gas in the rock failure process. The experimental results showed that the blasting stress wave is the direct reason for the formation of the crush zone and the blasting gas is the main driving force for the formation of the fracture zone. Cho et al. [11] used a numerical simulation method to study the effect of blasting stress waves with different waveforms on crack propagation in rock. The results showed that the crack propagation is mainly affected by the rising edge of the blasting stress wave, and the higher loading rate will increase the number of radial cracks.
In the study of the action effect of blasting gas, Kutter et al. [12] explored the action characteristics of the blasting gas and proposed a "gas wedge" effect of the blasting gas. It was believed that the blasting gas can form a quasi-static stress field inside the crack of the rock medium. Wang et al. [4] produced high-pressure gas by a mechanical method and wedged it into rock fissures to simulate the destructive effect of blasting gas on the rock. The results showed that under the action of high-pressure gas, the rock exhibited quasi-static failure characteristics with tensile fracture as the main failure mode. In addition, through theoretical derivation and analysis, Yang et al. [13] believed that the microcracks near the borehole gradually propagate under the driving pressure of the blasting gas, while the cracks farther from the borehole are further propagated under the combined action of the expansion pressure of the blasting gas and the in situ stress field. Trivino et al. [14] combined the FEM and the DEM methods to optimize the blasting parameters and carried out on-site blasting experiments. The data analysis showed that the main damage of the rock in the experiment was caused by blasting gas, indicating that it is still difficult to quantify the relative contribution of the blasting stress wave and blasting gas at present.
There are still different views on the proportion of the rock fragmentation effect caused by blasting stress waves and blasting gas and their distribution in time and space [14][15][16]. In this paper, the water jet test is used to calculate the water jet velocity and kinetic energy caused by the blasting of lead azide and to further analyze the energy distribution characteristics of the blasting stress wave and blasting gas. In addition, different materials are used to block the borehole in order to study the utilization efficiency of blasting energy under different borehole constraint conditions.

Experimental Design
The experimental setup of the water jet test is shown in Figure 1. Using stainless steel as raw material, the experimental test specimen shown in Figure 2 was machined. The horizontal hole was the borehole, and the vertical hole was a water injection hole. The borehole and the water injection hole were connected to each other. The water column, charge condition, and borehole constraint in the test specimen are shown in Figure 3. The diameter of the water injection hole was d 1 = 3 mm, the height of the water column in the hole was l = 55 mm, the mass of the water column was m = 0.39 g, and the diameter of the borehole was d 2 = 4 mm. The middle part of the borehole was the charge section, and the two sides were the blocking sections. The water column and the charge section were separated by a waterproof membrane in order to prevent water in the water injection hole from being immersed in the explosive in the borehole. In this experiment, the blasting energy was restrained and controlled by the blocking sections on both sides of the explosive. There were two kinds of blocking materials in the borehole-namely, plasticine and fine sand. The main components of plasticine are calcium carbonate, liquid paraffin, and glycerin. The density of plasticine is 1.7 g/cm 3 . The plasticine has strong plasticity and has a weaker constraint on the blasting energy. The fine sand was solidified after being mixed with glue, and the blasting energy was strongly constrained when it was used as the blocking material.
Energies 2020, 13, 5340 3 of 9 immersed in the explosive in the borehole. In this experiment, the blasting energy was restrained and controlled by the blocking sections on both sides of the explosive. There were two kinds of blocking materials in the borehole-namely, plasticine and fine sand. The main components of plasticine are calcium carbonate, liquid paraffin, and glycerin. The density of plasticine is 1.7 g/cm 3 . The plasticine has strong plasticity and has a weaker constraint on the blasting energy. The fine sand was solidified after being mixed with glue, and the blasting energy was strongly constrained when it was used as the blocking material.   The explosive used in the experiment was lead azide (Pb(N3)2), which was detonated by the high-voltage discharge of metal probes. According to the blocking material of the borehole, there were three experimental groups, namely: (1) both blocking materials A and B were fine sand mixed with glue, recorded as the experimental group with strong constraint; (2) blocking material A was plasticine and blocking material B was fine sand mixed with glue, recorded as the experimental group with medium constraint; (3) both blocking materials A and B were plasticine, recorded as the experimental group with weak constraint. With the charge amount as a variable, each group carried out the blasting experiments with the charge amount of C = 20, 30, 40, 50, 60, 70, and 80 mg.
After the preparation for the experiment was completed, the accent light, shown in Figure 1, was turned on, and the focus of the high-speed camera was adjusted. The high-speed camera was set to the post-trigger mode to start shooting, and then the detonating device was turned on to detonate the explosive through high-voltage discharge. Under the action of the blasting load, the water column in the water injection hole jetted out and the whole process was recorded by a high-speed camera. The recording speed of the high-speed camera was 20,000 fps, and the time interval between two  The explosive used in the experiment was lead azide (Pb(N3)2), which was detonated by the high-voltage discharge of metal probes. According to the blocking material of the borehole, there were three experimental groups, namely: (1) both blocking materials A and B were fine sand mixed with glue, recorded as the experimental group with strong constraint; (2) blocking material A was plasticine and blocking material B was fine sand mixed with glue, recorded as the experimental group with medium constraint; (3) both blocking materials A and B were plasticine, recorded as the experimental group with weak constraint. With the charge amount as a variable, each group carried out the blasting experiments with the charge amount of C = 20, 30, 40, 50, 60, 70, and 80 mg.
After the preparation for the experiment was completed, the accent light, shown in Figure 1, was turned on, and the focus of the high-speed camera was adjusted. The high-speed camera was set to the post-trigger mode to start shooting, and then the detonating device was turned on to detonate the explosive through high-voltage discharge. Under the action of the blasting load, the water column in the water injection hole jetted out and the whole process was recorded by a high-speed camera. The recording speed of the high-speed camera was 20,000 fps, and the time interval between two successive photos was 50 μs. The explosive used in the experiment was lead azide (Pb(N 3 ) 2 ), which was detonated by the high-voltage discharge of metal probes. According to the blocking material of the borehole, there were three experimental groups, namely: (1) both blocking materials A and B were fine sand mixed with glue, recorded as the experimental group with strong constraint; (2) blocking material A was plasticine and blocking material B was fine sand mixed with glue, recorded as the experimental group with medium constraint; (3) both blocking materials A and B were plasticine, recorded as the experimental group with weak constraint. With the charge amount as a variable, each group carried out the blasting experiments with the charge amount of C = 20, 30, 40, 50, 60, 70, and 80 mg.
After the preparation for the experiment was completed, the accent light, shown in Figure 1, was turned on, and the focus of the high-speed camera was adjusted. The high-speed camera was set to the post-trigger mode to start shooting, and then the detonating device was turned on to detonate the explosive through high-voltage discharge. Under the action of the blasting load, the water column in the water injection hole jetted out and the whole process was recorded by a high-speed camera. The recording speed of the high-speed camera was 20,000 fps, and the time interval between two successive photos was 50 µs.

Phenomenon Analysis
The blasting stress wave and the blasting gas are the two main motivations for rock fragmentation in rock blasting. The experiments mainly studied the utilization characteristics of blasting energy under different blocking constraint conditions. In order to distinguish the effects of blasting stress wave and blasting gas, the verification experiment was carried out before the above three experimental groups were performed. The test specimen of the verification experiment is shown in Figure 4; the vertical water injection hole and the horizontal borehole were not connected, and there was a separation distance of 2 mm between the two holes. Since the water injection hole and the borehole were not connected, the blasting gas could not enter the water injection hole, and the blasting gas could not exert an effect on the water column. Therefore, it can be considered that the effect of the blasting gas on the water column was shielded, and the water column was only subjected to the blasting stress wave. The high-speed camera was used to photograph and record the experimental process of the verification experiment group. It was found that regardless of the charge amount or the blocking constraint, the water column in the water injection hole did not have a jet phenomenon, indicating that the blasting stress wave did not change the mechanical energy of the water column. It can be concluded that under the experimental conditions of this paper, the effect of the blasting stress wave on the water column jet was basically negligible.
Energies 2020, 13, x FOR PEER REVIEW 4 of 8 three experimental groups were performed. The test specimen of the verification experiment is shown in Figure 4; the vertical water injection hole and the horizontal borehole were not connected, and there was a separation distance of 2 mm between the two holes. Since the water injection hole and the borehole were not connected, the blasting gas could not enter the water injection hole, and the blasting gas could not exert an effect on the water column. Therefore, it can be considered that the effect of the blasting gas on the water column was shielded, and the water column was only subjected to the blasting stress wave. The high-speed camera was used to photograph and record the experimental process of the verification experiment group. It was found that regardless of the charge amount or the blocking constraint, the water column in the water injection hole did not have a jet phenomenon, indicating that the blasting stress wave did not change the mechanical energy of the water column. It can be concluded that under the experimental conditions of this paper, the effect of the blasting stress wave on the water column jet was basically negligible. On the basis of the verification experiment, three experimental groups were carried out. Under the action of the blasting load, the water column in the water injection hole was jetted. Figure 5 shows a series of photos of water jet in the water injection hole under blasting load (weak constraint, C = 20 mg). The verification experiment proved that the blasting stress wave did not contribute to the jet of the water column. Therefore, it can be considered that the water jet in the water injection hole was caused by the action of the blasting gas. When t = 100 μs, the water column began to jet out of the water injection hole; when t = 200 μs, the water column continued to jet, and the length of the jetted water column was longer. During t = 0-200 μs, the overall shape of the water column was complete, showing an overall "lifting" motion state, and the overall motion state of the water column was coordinated. In this stage, the jet velocity of the water column reached its peak and the jet process was the most stable. When t > 300 μs, the overall shape of the jetted water column changed and the jet velocity of each section of the water column was inconsistent. The middle part of the jetted water column became thinner, the upper part of the jetted water column was gradually atomized, and the motivation state of the jetted water was more complicated and variable. After the experiment, the states of the blocking materials in the test specimen were checked one by one. It was found that the On the basis of the verification experiment, three experimental groups were carried out. Under the action of the blasting load, the water column in the water injection hole was jetted. Figure 5 shows a series of photos of water jet in the water injection hole under blasting load (weak constraint, C = 20 mg). The verification experiment proved that the blasting stress wave did not contribute to the jet of the water column. Therefore, it can be considered that the water jet in the water injection hole was caused by the action of the blasting gas. When t = 100 µs, the water column began to jet out of the water injection hole; when t = 200 µs, the water column continued to jet, and the length of the jetted water column was longer. During t = 0-200 µs, the overall shape of the water column was complete, showing an overall "lifting" motion state, and the overall motion state of the water column was coordinated. In this stage, the jet velocity of the water column reached its peak and the jet process was the most Energies 2020, 13, 5340 5 of 9 stable. When t > 300 µs, the overall shape of the jetted water column changed and the jet velocity of each section of the water column was inconsistent. The middle part of the jetted water column became thinner, the upper part of the jetted water column was gradually atomized, and the motivation state of the jetted water was more complicated and variable. After the experiment, the states of the blocking materials in the test specimen were checked one by one. It was found that the blocking material of the fine sand mixed with the glue was basically non-destructive and did not flush out of the borehole. However, the blocking material of the plasticine was significantly compressed and flushed out of the borehole.

Data Analysis
The maximum jet velocity vmax of the water column was obtained by measuring the change of the height h of the jetted water column in t = 0-200 μs. The work of the blasting load on the water column is: where W is the work of the blasting load on the water column; ΔEk is the change of the kinetic energy of the water column, the initial kinetic energy of the water column being 0; ΔEg is the change of the gravitational potential energy of the water column; and Wf is the work of frictional resistance between the water column and the wall of the water injection hole during the jet process. When 0.39 g of water rises by 1 cm, the gravitational potential energy of the water column increases by 3.9 × 10 −5 J, which is much smaller than the increase in kinetic energy. Therefore, compared with the change of the kinetic energy ΔEk of the water column, the change of the gravitational potential energy ΔEg of the water column and the work of frictional resistance Wf can be neglected. Therefore, Equation (1) can be simplified as: where m is the mass of the water column, m = 0.39 g, and vmax is the maximum jet velocity of the water column.
In the above analysis, the recording speed of the high-speed camera was extremely fast, and the maximum jet velocity of the water column can be calculated as: where Δh is the change in the height of the jetted water column during t = 100-200 μs and Δt is the time interval, Δt = 100 μs. According to Equations (2) and (3), the maximum jet velocity vmax and the work of blasting load W with different charge amount C under different constraint conditions, shown in Table 1, were calculated.
According to the data in Table 1, the relationship and the corresponding fitting curves between the charge amount C and the maximum jet velocity vmax were obtained and are shown in Figure 6.

Data Analysis
The maximum jet velocity v max of the water column was obtained by measuring the change of the height h of the jetted water column in t = 0-200 µs. The work of the blasting load on the water column is: where W is the work of the blasting load on the water column; ∆E k is the change of the kinetic energy of the water column, the initial kinetic energy of the water column being 0; ∆E g is the change of the gravitational potential energy of the water column; and W f is the work of frictional resistance between the water column and the wall of the water injection hole during the jet process. When 0.39 g of water rises by 1 cm, the gravitational potential energy of the water column increases by 3.9 × 10 −5 J, which is much smaller than the increase in kinetic energy. Therefore, compared with the change of the kinetic energy ∆E k of the water column, the change of the gravitational potential energy ∆E g of the water column and the work of frictional resistance W f can be neglected. Therefore, Equation (1) can be simplified as: where m is the mass of the water column, m = 0.39 g, and v max is the maximum jet velocity of the water column.
In the above analysis, the recording speed of the high-speed camera was extremely fast, and the maximum jet velocity of the water column can be calculated as: where ∆h is the change in the height of the jetted water column during t = 100-200 µs and ∆t is the time interval, ∆t = 100 µs. According to Equations (2) and (3), the maximum jet velocity v max and the work of blasting load W with different charge amount C under different constraint conditions, shown in Table 1, were calculated. According to the data in Table 1, the relationship and the corresponding fitting curves between the charge amount C and the maximum jet velocity v max were obtained and are shown in Figure 6. Obviously, as C increased and the constraint strength enhanced, the v max of the water column gradually increased. The C and the v max of the water column satisfy a quadratic polynomial relationship. The fitting relationship under the strong constraint condition is v max = −0.07C 2 + 13.74C, the fitting relationship under the medium constraint condition is v max = −0.035C 2 + 10.29C, and the fitting relationship under the weak constraint condition is v max = −0.05C 2 + 9.94C.  Furthermore, according to the data in Table 1, the relationship and the corresponding fitting curves between the charge amount C and the work of blasting load W were obtained and are shown in Figure 7. It can be seen from the fitting curve that W and C satisfy a linear relationship. The fitting relationship under the strong constraint condition is W = 0.98C, the fitting relationship under the medium constraint condition is W = 0.79C, and the fitting relationship under the weak constraint condition is W = 0.50C. The slope of the fitting curve indicates the work of blasting load of per unit mass explosive under the current constraint condition, which can be called the unit mass work of the explosive Wu. Thus, the Wu under the strong, medium, and weak constraint conditions is 0.98 J/mg, 0.78 J/mg, and 0.50 J/mg, respectively, and these works are all contributed by the blasting gas. It can be seen that with the weakening of the constraint condition, the Wu is gradually reduced. It should be noted that an approximate calculation method was adopted for the work of blasting load, ignoring the change of the gravitational potential energy of the water column and the work of frictional resistance between the water column and the wall of the water injection hole during the jet process. Therefore, the actual unit mass work of the explosive should be greater than the above calculated value. Furthermore, according to the data in Table 1, the relationship and the corresponding fitting curves between the charge amount C and the work of blasting load W were obtained and are shown in Figure 7. It can be seen from the fitting curve that W and C satisfy a linear relationship. The fitting relationship under the strong constraint condition is W = 0.98C, the fitting relationship under the medium constraint condition is W = 0.79C, and the fitting relationship under the weak constraint condition is W = 0.50C. The slope of the fitting curve indicates the work of blasting load of per unit mass explosive under the current constraint condition, which can be called the unit mass work of the explosive W u . Thus, the W u under the strong, medium, and weak constraint conditions is 0.98 J/mg, 0.78 J/mg, and 0.50 J/mg, respectively, and these works are all contributed by the blasting gas. It can be seen that with the weakening of the constraint condition, the W u is gradually reduced. It should be noted that an approximate calculation method was adopted for the work of blasting load, ignoring the change of the gravitational potential energy of the water column and the work of frictional resistance between the water column and the wall of the water injection hole during the jet process. Therefore, the actual unit mass work of the explosive should be greater than the above calculated value.
Energies 2020, 13, 5340 7 of 9 0.78 J/mg, and 0.50 J/mg, respectively, and these works are all contributed by the blasting gas. It can be seen that with the weakening of the constraint condition, the Wu is gradually reduced. It should be noted that an approximate calculation method was adopted for the work of blasting load, ignoring the change of the gravitational potential energy of the water column and the work of frictional resistance between the water column and the wall of the water injection hole during the jet process. Therefore, the actual unit mass work of the explosive should be greater than the above calculated value.   A large number of underwater explosion experiments that study the energy distribution characteristics of blasting stress wave and blasting gas explosions indicate that the total energy E 0 of the blasting stress wave and blasting gas generated by per unit mass explosive is approximately equal to the explosive heat Q v . The explosive heat Q v of Pb(N 3 ) 2 is 1.524 J/mg, as obtained by the calorimetry test. Therefore, it can be considered that the total energy of the blasting stress wave and blasting gas generated per unit mass explosive of Pb(N 3 ) 2 is E 0 ≈ Q v = 1.524 J/mg. According to the above experimental analysis results, the ratio of W u and E 0 is called the utilization efficiency of the total energy η t . The η t under the strong, medium, and weak constraint conditions was respectively obtained as 64%, 51%, and 33%. As the constraint condition was weakened, the η t also gradually reduced. Under the strong constraint condition, the blocking material is basically non-destructive and does not flush out of the borehole, and it can be considered that the blasting gas energy is completely converted into the work for the jetted water column. The water jet is caused by the action of the blasting gas, and the blasting energy is mainly composed of the blasting gas energy and the blasting stress wave energy. Based on this, the blasting gas generated by the explosion of Pb(N 3 ) 2 accounted for 64% of the E 0 , and the blasting stress wave energy accounted for 36% of the E 0 . This indicates that the blasting energy is mainly contained in the blasting gas, which is basically consistent with the conclusions of previous research [17]. Furthermore, the utilization efficiencies of the blasting gas energy η g under the conditions of strong, medium, and weak constraint were 100%, 80%, and 52%, respectively.

Conclusions
Rock blasting fracture is the result of the combined action of the blasting stress wave and the blasting gas. The action effect of the blasting stress wave and blasting gas is an important part of the basic theory of rock blasting. In this paper, the designed experimental test specimen was used to shield the interference of the blasting stress wave from the experimental results, and the energy distribution characteristics of the blasting gas during the blasting process were studied.
Under the strong constraint condition, the blasting gas energy was basically converted into the kinetic energy of the jetted water column. The calculation and analysis of the experimental results show that the blasting gas energy of Pb(N 3 ) 2 and the blasting stress wave energy of Pb(N 3 ) 2 accounted for about 64% and 36% of the total energy, respectively. In addition, the utilization efficiencies of the total blasting energy under the strong, medium, and weak constraint conditions were 64%, 51%, and 33%, respectively, and the utilization efficiencies of the blasting gas energy were 100%, 80%, and 52%, respectively. It can be seen that as the constraint condition was weakened, the utilization efficiency of the total blasting energy and the utilization efficiency of the blasting gas energy were both reduced. Therefore, the blocking constraint effect of borehole is crucial for the efficient use of blasting energy in rock blasting engineering. It is worth noting that the conclusions of this paper are mainly based on the blasting experiment with a small quantity of charge, and there is still a certain gap with actual engineering applications. In addition, limited to experimental conditions, this paper only used Pb(N 3 ) 2 as an explosive to carry out experimental research, and approximate treatment was used in the calculation of the blasting energy of the explosive. Therefore, the universality of the relevant conclusions is still worthy of further study. However, this work provides a new idea for studying the energy distribution characteristics of rock blasting, and reveals the effect of the borehole blocking condition on the utilization of blasting energy to some extent.