The main analysis object is nonlinear dynamic analysis, which is very suitable for the explosive explosion, vibration and shock, and other issues. Considering that the initial ground stress is much smaller than the compressive stress formed by the detonation gas, the initial ground stress is neglected during the numerical simulation.
In the numerical simulation process, the smooth particle flow method is used to carry out a two-dimensional numerical simulation of the presplitting blasting of the energy-concentrating tube. In the process of simulating material large deformation in the numerical method based on the grid, it is easy to terminate the calculation due to grid distortion, and it is difficult to simulate the problem with a strong impact discontinuity. Explosion, penetration, and high-speed collision involve large deformation, the strong impact, and the interaction process of the material interface; the smooth particle flow method makes up for these problems based on the grid computing method [ 20 , 21 ].
Explosives use mineral emulsion explosives. The pressure-volume relationship of explosives during detonation is expressed by the JWL equation of state as where P is the pressure of detonation products, A , B , R 1 , R 2 , and omega are the material constants determined by experiments, V is the relative volume of detonation products, and E 0 is the initial internal energy density of detonation products.
Parameters of explosives and the JWL equation of state are shown in Table 1. The polyenergy material is selected from the PVC pipe, and the specific parameters of the constitutive equation using the plastic follow-up model are shown in Table 2.
The plastic follow-up model is a hybrid model of isotropic, creep hardening or isotropic and follow-up hardening, which is related to strain rate and can be considered for failure. C and p are copper-Symonds strain rate parameters. E p is plastic hardening modulus, , E tan is the tangent modulus. Specific parameters of shaped charge materials are shown in Table 2. The rock material in the model uses the Johnson-Holmquist II JH2 model to study the crack propagation of rock mass blasting process under blast loading.
Fine rock sandstone is selected as the reference to the rock parameters. The specific parameters are selected as shown in Table 3. In this paper, LS-DYNA software was used to simulate the influence of different shaped energy angles on the blasting, and the length and angle of the crack were analyzed.
The JH2 model used in the rock materials in the numerical model is a nonhardened material model. Its yield surface and failure surface coincide. Generally, the equivalent stress is used to express the elastic limit of the failure criterion.
The yield surface expression in the model includes the normalized pressure and the maximum normalized tensile hydrostatic pressure. Therefore, in numerical simulation, the damage is the result of the combined effect of the two.
In addition, the damage itself is a microscopic description of the crack, and the macrocrack is also caused by the action of a large number of microcracks. Therefore, the damage in the numerical simulation results would be used to describe macroscopic cracks. In order to verify the influence of the shaped energy angle on the effect of the shaped energy blasting, a single blast hole with different angles of shaped energy angle was numerically simulated with reference to ordinary blasting.
After forming the shear stress failure zone at 0. As the blasting progresses, the crack tip was continuously unstable and the crack was continuously caused, expanding until the crack runs through.
The direction was cracked while presenting a single horizontal crack crack I; crack II. It could be seen from Figure 7 b that, during the development of the equivalent stress in the blasting process, stress concentration occurred near the shaped energy hole immediately after the explosive was detonated, and the nearby rock was subjected to the tensile stress.
As the blasting progresses, the crack tip was continuously destabilized, causing the crack to expand continuously until the crack penetrates, presenting a single horizontal crack pattern. Figure 8 b shows the evolution of the equivalent stress during the blasting process. As shown in Figure 8 b , immediately after the detonation of the explosive, stress concentration occurs near the shaped energy hole, but four stress concentration regions symmetric with the direction of shaped energy appear immediately, and the nearby rock is subjected to tensile stress.
It can be seen from the figure that the stress in the direction of the shaped energy hole is negative. As the blasting progresses, the crack tip is continuously destabilized, causing the crack to expand continuously until the crack penetrates, and the equivalent stress tends to zero, forming a symmetric crack.
In the initial stage, microcracks are formed near the shaped energy holes, but with the continuous movement of the explosive particles, four symmetric cracks crack I, crack II, crack III, and crack IV appearing at different angles to the horizontal crack appear, and with time, the symmetric crack begins to dominate the cracking direction of the crack.
Figures 9 b and 10 b show the evolution of the equivalent stress during the blasting process. Immediately after the detonation of the explosive, stress concentration occurred near the shaped energy hole, but four stress concentration areas symmetrically with the direction of the energy accumulation appeared immediately, and the nearby rock was subjected to tensile stress, which can be seen from the figure. The hole direction stress is negative. As the blasting progresses, the crack tip is continuously destabilized, causing the crack to expand continuously until the crack penetrates, and the equivalent stress tends to zero, forming a symmetric shear crack.
In Figure 11 b , in the middle, the peak lengths of the two cracks are shown. After 0. In Figure 11 c , the length of crack propagation can be seen as a function of time. The initial expansion speed of the crack is the same, and the slope is consistent, but at the end of the latter, the crack propagation speed is greater than the speed of the right crack. The shaped energy device can be obtained with a satisfactory blasting effect.
From the figure, we can see the four crack length peaks, corresponding to four cracks. In Figure 12 b , the peak lengths of the four cracks are shown.
The crack length also increases with time. Four packs of crack length are obtained from the figure, indicating that four cracks appear at four angles, and four crack length peaks are shown in Figures 13 b and 14 b. The crack tip cracking direction is 0. The symmetry crack began to dominate the cracking direction of the crack. In the theoretical analysis, the increase of the shaped energy angle is the increase of the stress intensity factor and the energy release rate at the crack tip.
When the energy release rate is far greater than the crack propagation resistance, excess energy will generate new cracks, causing cracks to bifurcate. In the theoretical analysis, the J-integral theory is used to calculate the The above angle values were measured from the shaped energy blast damage development map and were close to the theoretical value of Therefore, the numerical simulation agrees with the theoretical analysis conclusion.
The working face of Hecaogou No. The main coal seam thickness of this working face is 0. Roadway support design is shown in Figure Combined with the results of numerical simulations, when the shaped energy angle is greater than or equal to 35 degrees, the crack would produce a bifurcation phenomenon.
The field experiment used the method of interval blasting. During the experiment, one shaped tube was used for each blast hole, and three rolls of mining emulsion explosives were installed in the middle of the shaped tube. The charging structure diagram is shown in Figure Since the cracks formed between the blast holes cannot be visually observed after the blasting, the CXK6 mine intrinsically safe drilling imager was used to peek at the site, as shown in Figure It can be seen that after the explosives exploded, obvious continuous cracks were generated from the interval holes to the bottom of the holes, and the cracks extended along the line of the gun holes, indicating that continuous cut surfaces can be formed between the holes.
The stress intensity factor of the crack tip will increase with the increase of the energy concentration angle, and the increasing trend will become more and more significant. It will also release more energy in the energy concentration direction. The crack and main crack will be The upper crack is bifurcated. The numerical results, field experiments, and theoretical analysis results agree well. The authors declare that there are no conflicts of interest regarding the publication of this paper.
In addition, thanks are due to all the people who contributed to the research and the manuscript. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles. Journal overview. Special Issues. Academic Editor: Ayman S. Received 16 Sep Revised 19 Feb Accepted 24 Feb Published 20 May Abstract Shaped energy blasting has been widely used in the field of geotechnical engineering because of its good orientation and high energy utilization.
Introduction With the widespread application of coal-free column cutting and roadway technology and the improvement of underground engineering, blasting excavation requirements, the requirements for the connectivity of cracks, and the linearity of cracks in the direction of shaped energy in shaped energy blasting are also increasing. Principle of Concentrated Energy Blasting The dynamic process of bidirectional cumulative tensile blasting is mainly in the following stages: in the initial stage, after the explosive is detonated, high temperature and high-pressure gas are rapidly generated, and the shock wave formed by the explosion directly impacts the rock mass through the shaped energy hole so that the surrounding of the shaped energy hole the rock is fractured.
Figure 1. Principle and device of bidirectional cumulative tension blasting. Figure 2. Schematic diagrams of shaped energy angle of bidirectional cumulative tension blasting.
Figure 3. Schematic diagram of bidirectional cumulative tension blasting. Figure 4. Figure 5. Table 1. Table 2. Table 3. Figure 6. Damage evaluation and effective stress evaluation for single hole concentrated energy blasting.
Figure 7. Figure 8. Figure 9. Figure Table 4. Illustration of single hole charge. Crack propagation after shaped energy blasting.
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Reprints and Permissions. Mohamed, H. Int J Steel Struct 18, — Download citation. Received : 10 March Accepted : 07 September Published : 25 April Issue Date : June Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative. Skip to main content. Search SpringerLink Search. Abstract This paper focuses on the crack propagation angle effects on the stress intensity factors of a 3-D semi-elliptical surface crack in tubular T-joints.
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