Propagation Characteristics of Explosion Wave and Explosion Gas in Blast-Hole

. In order to explore the propagation characteristics of explosion wave and gas in blast-hole, design a model to simulate blast-hole charge in the laboratory, adopted a high-speed schlieren experiment system used to study the evolution characteristics of explosion wave feld under two kinds of charge structures. Te results showed similar explosion wave velocities for the two cartridges, the explosion wave was refected when it reaches the hole wall, and the refected wave velocity was lower than an incident wave. Te explosion gas tends to cluster and spread in a cutting direction, resulting in intensifed destruction in that direction. Te explosion wave frst emerges in the direction of the slits, and then moves towards the blast-hole walls, which indicates that the explosion energy can be accumulated in the slit direction and cause directional destruction of the medium. To study this process in detail, establish numerical model for the propagation of explosive in the hole. Te results indicated that the detonation products frst come out in the direction of the slits and then go around towards other areas in a distribution that is consistent with the observations by high-speed schlieren photography.


Introduction
Te structure of a cutting seam cartridge makes a signifcant contribution in delivering directional explosive cracks. For this reason, many studies have examined the principles of the cutting seam cartridge in rock blasting. As early as the 1970s, it has been proposed a method to create directional cracks in rock using axially slitted tubular cartridges in blast-holes. Fourney et al. [1,2] conducted a series of explosion experiments was performed with slitted tubular cartridges, which showed that cracks can be controlled even under explosive conditions. Cho et al. [3] performed model tests and numerical simulations, observed signifcantly directed blast-hole grooves that were conducive to the formation of a fat crack surface. Isakov [4] proposed a loading method in which an axially grooved solid shell was positioned along the blast-hole wall; experiments revealed that the crack distribution caused by an explosion may be infuenced by shell strength, shell thickness, and the initial burst pressure of the cavity. Te caustic specks at the crack tip can be observed in the dynamic caustic experiment system, and the crack propagation velocity and stress intensity factor can be calculated [5,6]. Yang et al. [7,8] studied the directional crack characteristics of a cutting seam cartridge, and the transmission mechanism of the explosion wave of the cutting seam cartridge with diferent uncoupling coefcients. Yue et al. [9][10][11] analysed the interaction between cracks for a double-hole directional crack-controlled explosive using the caustic method, also studied the application of the cutting seam cartridge. Guo et al. [12] studied the change of the mechanical parameters of the crack tip created by explosive when the crack approaches a hole defect. Yang and Wang [13,14] studied cracks by the cutting seam cartridges of diferent structures using the caustic method and numerical analysis software. Te experiments found that the cutting seam cartridge can cause directional cracks in the medium. Ma and An [15] used the J-H material model of LS-DYNA numerical simulation software, studied the explosion efect under diferent groove angles in grooved explosive.
Te high-speed schlieren experiment system can monitor the density change of the air feld under disturbance [16,17]. Yang et al. [18,19] adopted this device and studied the evolution of an explosive wave feld in an exposed air medium. Zuo et al. [20] studied the explosion wave propagation characteristics of cylindrical explosive at diferent initiation positions, and obtained the included angle range of explosion shock wave incident on the hole wall, revealed the distribution characteristics of explosion cracks in diferent areas. Ambrosini et al. [21,22] using background optical directional schlieren technique, solved the visualization of convective heat transfer, improved the accuracy of temperature measurement by using the windowed Fourier transform method. Zhang [23], using high-speed schlieren photography, overpressure measurement, and numerical simulation were applied to study the shock wave propagation of the charge in a pipe with holes, it turns out that the blast wave in the direction of the hole was released more fully.
However, most studies on the explosion wave of a cartridge have been speculative proposals based on explosive theories, and there is a striking lack of comprehensive experimental studies on the explosion wave of a cartridge. Te goal of this work was to capture the fne structural features of a cartridge explosion wave during propagation using the high-speed schlieren photography technique. Te dynamic changes in the explosion wave and explosion gas in the blasthole were also recorded using this technique. Te diferences in transmission between the common structure package and the cutting seam cartridge were compared and analysed. Te results from the high-speed schlieren photography and numerical analysis provide insight into the dynamic change in the explosion wave of a cartridge.

Experimental Details.
Te experimental loading design included a common cartridge and a cutting seam cartridge. Te material of the cutting seam cartridge is stainless steel pipe, the selected explosive is diazodinitrophenol and the dosage is 200 mg. It used a plexiglass tube with a diameter of 40 mm to simulate the blast-hole and studied the transmission characteristics of the explosion wave in the blasthole. Te cartridge was hoisted at the center inside the plexiglass tube. Te plexiglass tube and the cartridge were oriented in a direction parallel to the square. Figure 1 shows the common cartridge and cutting seam cartridge for the schlieren experiment. Figure 2 shows the structure and schematic diagram of the high-speed schlieren experiment. Te composition and testing principle of the experimental system can be referred to the literature [20]. It should be emphasized that the shooting speed of the high-speed camera was 100000 pictures/second during the experiment.

Distribution of Explosion Products in the Blast-Hole.
Figures 3(a) and 4(a) show the distribution of explosion products in the blast-hole. Te distribution of explosion gas in the hole wall can be observed obviously. Te experimental results reveal a wide distribution of the explosion products of the common cartridge on the blast-hole. In contrast, the explosion gas of the cutting seam cartridge exhibits a regular distribution on the blast-hole. Te explosion products were concentrated in the slit direction, and those in other directions were not concentrated. Te explosion gas plays a very important role in rock explosion. Te distribution direction of the explosion products also refects the formation and expansion of the initial crack of the blasthole wall.
In order to better compare the comparison results under the two charging modes, the distribution range of explosive products in diferent areas on the blast-hole wall was divided into four quadrants, with 90°as a quadrant, in which the I and III quadrants were the direction of slit cutting of the    In order to further analyse the distribution characteristics of explosive products. In this paper, fractal dimension is used to characterize the distribution of explosive products on the blast-hole wall. Te box dimension of fractal dimension is used to calculate the possession of explosive products in the selected area. Te box dimension is shown in the following formula [24]: N δ k is the number of boxes containing divided areas; D is the fractal dimension of regional explosion products. δ k is the edge length of the small boxes. Figure 5 shows the fractal dimension results of explosive products in diferent regions. I and III quadrants were the area which direction of slit, and the II and IV quadrants were area which vertical direction of slit. Te distribution of the explosive products of slit charge is relatively concentrated in the I and III quadrants and the fractal dimension was 1.5931 and 1.3785, with an average of 1.4858. However, the distribution of explosion products in II and IV quadrants were less, and the fractal dimension was 0.8202 and 1.0371, with an average value of 0.9287. Te average value of explosion products in slit direction was increased by 60.0% compared with that in vertical slit direction. Te fractal dimension of common cartridge explosive products in the four quadrants is relatively uniform. Trough the above analysis, the cutting seam cartridge has the ability to accumulate explosive products, which indicates that the explosion energy can be accumulated in the slit direction, it can directional destruction of the medium.  Figure 6 shows the transmission of the explosion wave and explosion gas for the common cartridge. Te explosion wave is obvious at 30 μs, followed by explosion gas. Te explosion wave begins to separate from the explosion gas at 40 μs. Te explosion wave further develops and the explosion gas travels at a lower velocity at 60 μs. Te explosion wave arrives at the blast-hole wall at 110 μs. Tis explosion wave is gradually refected and the refected explosion wave is substantially the same as the shape of the incident explosion wave at 150 μs. Te refected explosion wave further shrinks into the blast-hole until the refected explosion wave basically disappears at 200 μs. Te explosion wave is no longer visible at 380 μs. Te explosion gas arrives at the blast-hole wall at 770 μs, but is not evenly distributed.

Te Cutting Seam Cartridge Explosion Wave Process.
As shown by the explosion wave transmission of the common cartridge, when the common cartridge is detonated, the explosion wave and the explosion gas initially travel together, but gradually separate, with the explosion wave traveling faster than the explosion gas. Terefore, the explosion wave frst reaches the blast-hole wall, and forms a refected explosion wave that travels inside the blast-hole. However, only one refected explosion wave can be observed under the experimental conditions. Te explosion gas reaches the blast-hole wall after the explosion wave, and its arrival at the blast-hole wall is uneven, so the explosion gas is not signifcantly refected.   Shock and Vibration Figure 7 shows the transmission of the explosion wave and explosion gas of the cutting seam cartridge. Te explosion wave is obvious to the right and left of the slit at 30 μs, and the explosion wave shape appears like a spindle, and the explosion gas develops from the slit. Te explosion wave to the right frst arrives at the blast-hole wall at 80 μs, and the explosion gas develops in the slitting direction in the shape of a spindle, and there is no explosion gas expansion of the vertical slit. Te refected explosion wave shrinks inward in a similar elliptical shape at 120 μs. Te explosion wave begins to disappear at 180 μs. Te explosion gas arrives at blast-hole wall at 310 μs. Te explosion wave in the direction of the slit begins to expand around the blast-hole wall at 700 μs, and there is no signifcant refection of the explosion gas by the blast-hole wall.
Te explosion wave frst travels in the direction of the slit, and explosion gas released linearly along the slit direction. Te explosion wave travels faster than the explosion gas, and the explosion wave is refected after reaching the blast-hole wall, forming a refected explosion wave that shrinks inside the blast-hole.
Te cutting seam cartridge and the common cartridge were compared using the schlieren photography technique. Te explosion wave frst releases energy in the slit direction, and the formed "diversion" of the explosion wave causes the initial damage to the blast-hole wall, further damage occurs due to the quasi-static pressure of the high-pressure explosion gas. Figure 8(a) shows the change in the expansion velocity of the explosion wave and the explosion gas of the common cartridge. As shown in the fgure, the expansion velocity of the explosion gas is lower than that of the explosion wave. Within the 0∼120 μs time range, the explosion wave travels from center to the sides, and refected by the blasthole wall at 120 μs, forming a refected explosion wave. Tere is a velocity peak in this process, in which the refected explosion wave shrinks inward. Also, the velocity peak explosion wave is far lower than initial explosion wave. Te explosion gas velocity is rapidly attenuated within 60 μs, and then the travel velocity of the explosion gas is maintained at about 60 m/s after 60 μs. Figure 8(b) shows the speed change of cutting seam cartridge. Te explosion wave is refected at 80 μs, between 80 and 130 μs, there is a brief zone of velocity increase, and then gradually decrease. Compared with the velocity curve of the common cartridge, the biggest diference lies in the velocity curve of the explosion gas.

Material Model and Parameters.
Te numerical analysis software adopts AUTODYN [25]. Figure 9 shows the calculation model. Since schlieren experiment can only refect the propagation characteristics of explosives in the gun hole from the small-scale model experiment in the laboratory, in order to truly refect the actual conditions, a numerical simulation model in line with the actual construction is established. Te explosive diameter is 32 mm, the thickness of the slitting pipe is 2 mm, the incision is 4 mm, the inner diameter of the simulated blast-hole is 45 mm, and the thickness is 3 mm. Several pressure measuring points were arranged in the direction of the slit and vertical slit, of which points 1-5 were in the direction of slit and point 6-10 were in the direction of the vertical slit.

Shock and Vibration
Air is modeled as an ideal gas, the explosive used in this calculation is pentaerythritol tetranitrate (PETN), see References [19] for specifc parameter settings.
Te slitting pipe and blast-hole were made of steel, constitutive model used the Steinberg-Guinan strength model and the Mie-Gruneisen equation of state. Te shear modulus G is shown in the following formula [26]: where T 0 and G 0 are the reference temperature and shear modulus; G ′ T and G ′ P are constants of selected material; P is the pressure; k � ρ/ρ 0 . Te equation relationship of yield stress Y with efective shaping strain ε P can be expressed in the following formula: (3) and the following relation is satisfed t=0 μs t=30 μs t=40 μs t=60 μs t=80 μs t=100 μs t=120 μs t=160 μs t=180 μs t=310 μs t=700 μs t=1650 μs  Shock and Vibration where Y ′ P , β, and n are material constants. Mie-Gruneisen equation of state, the expression equation shown in the following formula [27]: where c is coefcient number of Gruneisen, v reference volume, e is internal energy, and the expression is c � c 0 /k, where c 0 is the reference value, e r and P r are the internal energy and pressure, the equation are shown in formulas (6) and (7): where c 0 is the speed of sound and S is the material parameter. Specifc parameters are shown in Table 1: Figure 10 shows the explosion gas distribution of the cartridge in the simulated blast-hole. Te distribution of explosion gas is highly approximate with the experimental results obtained by high-speed schlieren photography. Te explosives considered in the numerical simulation difer from that used in real experiments in terms of explosive type, charge density, and explosion velocity. At the initial explosion stage, the explosion gas frst expands in the slitting pipe, and when the explosion gas travels to the outer edge of the slit with a strong pressure wave, eddy currents were generated at both end faces of the outer wall of the slit by explosion wave, making the explosion gas travel in the form of a "W." Amid the expansion of the slitting pipe, a large amount of explosion gas bursts out along the slit. Te expansion pattern of the explosion gas that reaches the blasthole wall is highly consistent with that observed in the highspeed schlieren images, and the explosion gas expands along both sides of the blast-hole wall.

Explosion Wave Transmission in the Blast-Hole.
Explosion wave transmission inside the blast-hole is shown in Figure 11. At the beginning, the explosion wave of the explosives in the chemical reaction is the same as that of the explosives without the slitting pipe. Te explosion wave mass point is distributed in the form of a sphere. Te explosion wave and explosion gas at this point travel together and do not disturb the slitting pipe. Te explosion wave interacts with the entire slitting pipe, instantaneously loading the pipe wall and causing a high strain rate, which causes the slitting pipe to expand at a high degree. Amid the expansion, only a small fraction of the explosion gas and explosion wave travel from the slit, as shown in the fgure. Te slitting pipe further expands under the impact of the explosion wave. A portion of the explosion wave travels around the outer pipe wall, and a portion of the explosion wave impacts the surrounding medium directly in front of the slit direction. Te whole expansion process is similar with the experimental results. Te explosion wave interacts with the blast-hole wall, and high pressure is generated at the wall of the blast-hole, allowing the fow of explosion products along the wall. Figure 12 shows the pressure curve of each monitoring point. Figure 12(a) shows the explosion pressure changes of slit. Points 1-3 were the internal points. Te frst is caused by the detonation transfer pressure of the explosive when it is detonated, the second by the refected pressure of the slit tube wall, and the third by the refected pressure of the blasthole wall. Point 4 is located outside the cutting seam, and no second fuctuation occurs during the fuctuation process. It can be seen from the pressure curve of point 5 that there were have three fuctuations. Figure 12(b) shows the explosion pressure changes in the vertical direction of cartridge. Points 6-8 were the internal observation points. Compared with the corresponding pressure points 1-3, the pressure of the frst peak is basically the same, but the peak of the refected pressure in the second is very diferent, generally higher than the points 1-3 the second peak pressure. Te pressure fuctuation of point 9 and point 10 were caused by two parts, one part was caused by explosion gas fows around the blast-hole wall, the other part was caused by the slitting pipe expansion of internal pressure.

Conclusion
Te goal of this work was to capture the fne structural features of a cartridge explosion wave during propagation using the high-speed schlieren photography technique, and the following conclusions are obtained as follows: (1) Compared with the common cartridge, the cutting seam cartridge can gather explosion gas, leading to expansion of the explosion gas in a specifc direction, leading to enhanced damage to the medium in that direction. (2) Te explosion wave is refected by the blast-hole wall, but the explosion gas reaches the blast-hole wall in an uneven manner without being signifcantly refected. Te cartridge explosion wave frst travels in the slit direction, and the explosion gas expands in an linearly spread form along the slit direction. (3) Te explosion gas mainly impacts and gathers in the slit direction, and then travels around in other directions. Te explosion wave propagates speeds is similar of two cartridges, however, the propagation speed of explosive gas in slit cartridge is signifcantly higher than that of ordinary cartridge. (4) Numerical simulation results verifed high speed schlieren experiment, the explosion wave frst releases energy in the slit direction because initial damage to the blast-hole wall. Further damage to the damaged blast-hole wall occurs due to the quasistatic pressure of the high-pressure explosion gas.

Data Availability
Te data used to support the fndings of this study are available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that there are no conficts of interest. Shock and Vibration 9