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One-step raise excavation with burn cut is a kind of technology which use the drilling and blasting method to excavate the raise quickly. Due to the limitation of the free surface in burn cut, determination of cut parameters such as the length of burden and diameters of empty hole and charge hole is important to achieve a good effect of cut blasting. Meanwhile, the choice of the cut model is also crucial to form a proper opening. In this study, a modified Holmquist-Johnson-Cook (HJC) model, in which the tension-compression damage model and tension-compression strain rate effect model are considered, is embedded in the LS-DYNA software to investigate the damage evolution of rock in cut blasting. A simplified numerical model of burn cut is built in the LS-DYNA. The numerical results indicate that there is a threshold value of the burden length to maximize the opening. The empty hole has the effect of transferring blasting energy, and the effect becomes more obvious with the increase of the hole size. Moreover, the linear charge density of the prime cut hole can affect the compression and tension damage. Further, the comparison among four typical burn cut models are conducted based on numerical results. It demonstrates that triangular prism cut and doliform cut, which have more empty holes arrangement surrounding the prime cut hole, are better than spiral cut and diamond cut that with less empty holes locating one side of the prime cut hole in terms of energy efficiency and damage zone control.

Because of the advantages of high efficiency, simple operation, and low cost, the drilling and blasting method has always been the main method in rock excavation engineering such as mining, tunneling, and underground space development. Unlike bench blasting, in which burden rock is directed towards two or more free surfaces, there are only one free surface in tunnel and raise excavation blasting. Thus, cut blasting is the most critical step in the process of tunnel and raise excavation since it can create an opening as a second free surface for the subsequent borehole blasting. In the process of cut blasting, the prime cut hole takes the empty holes as the free surface and swelling space, so the corresponding burden rock is subjected to high degree of constriction [

For the study of rock blasting, numerical simulation is more efficient and flexible compared with the theoretical derivation and field test. Therefore, numerical simulation has become the main technique to investigate the damage evolution mechanisms of rock blasting [

Although the damage evolution mechanisms of rock blasting have been studied by many researchers, little work has been conducted on the investigation of cut blasting. For this case, Xie and Lu [

In the present paper, in order to study the influence of cut parameters that include the burden and the diameter of the empty hole and prime cut hole on rock damage evolution, a simplified cut numerical model is established in LS-DYNA. A tension-compression damage model, which is improved by the author based on the original HJC model, is implemented into LS-DYNA and employed for the rock material [

In the damage evolution process of rock under blasting loading, the rock damage is affected by radial compressive stress, hoop tensile stress, and reflection tensile stress [

In addition, the strain rate effect, which can enhance the dynamic strength of material, is a characteristic of rock under dynamic load [

For brittle materials, the DIF induced by tensile load is higher than that induced by compressive load under the same strain rate. Therefore, the DIFs of tension and compression should be calculated, respectively, in the modified HJC model. Most of the strain rate effect models proposed by many researchers were exponential models [

In the original HJC model, the damage is induced by the accumulation of the plastic strain and the plastic volume strain, which can well reflect the compressive damage of rock. Details of the damage model of the original HJC model can be found in Johnson and Holmquist [

In the modified HJC model, the tension damage is described as an exponential softening model proposed by Weerheijm and Doormaal [

For the exponential softening model, the stress-strain curve of uniaxial tension is shown in Figure

Exponential stress-strain curve for uniaxial tension.

In order to avoid the discontinuity of the yield surface at the point of

Parameters of the modified HJC model.

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3471 | 32.09 | 46.6 | 2.51 | 0.64 | 173.1 | 8.72 | 0.04 | 1.0 |

57.7 | 0.0012 | 1.92 | 0.100 | 17.8 | 9.9 | 104.1 | 0.01 | 0.0017 |

In this study, the JWL EOS is used to calculate the pressure induced by detonation products of high explosives. The JWL EOS is expressed as

Parameters of explosive material and JWL EOS.

^{3}) | ||||||||
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1210 | 5660 | 9.7 | 214.4 | 0.182 | 4.2 | 0.9 | 0.15 | 4.192 |

In practice, the radial decoupling charge structure is usually applied in cut blasting to control the damage zone. In this study, the radial air-decoupling charge technique is implemented. Material type 9 of LS-DYNA (^{3} and 0.25 J/cm^{3}, respectively [

The damage evolution process of the prime cut hole blasting can be divided into 4 stages [

In this study, LS-DYNA, which is a well-known nonlinear dynamic commercial software, is used to simulate the process of rock damage under burn cut blasting. This software includes Lagrange, Eulerian, and Arbitrary Lagrangian-Eulerian (ALE) algorithm. The process of rock blasting can be regarded as the fluid-structure interaction between the explosive and rock. Thus, the ALE algorithm can be employed to model the fluid-structure interaction characteristic. The explosive and air are modeled with Euler mesh, and the rock material is modeled with Lagrangian mesh in the ALE algorithm. The interaction between explosive and rock is achieved by the keyword “

To study the damage evolution process of the prime cut hole with different cut parameters, a series of numerical simulation schemes are designed based on a simplified cut model which includes a prime cut hole and a large empty hole. The corresponding numerical model, with the dimension of

Prime cut blasting numerical model geometry and boundary conditions.

The variables of cut parameters consist of length of the burden rock (

Numerical simulation schemes.

Schemes | Air layer (mm) | ||||
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1 | 170 | 250 | 110 | 1.737 | 10 |

2 | 220 | 250 | 110 | 1.371 | 10 |

3 | 270 | 250 | 110 | 1.132 | 10 |

4 | 320 | 250 | 110 | 0.964 | 10 |

5 | 370 | 250 | 110 | 0.840 | 10 |

6 | 420 | 250 | 110 | 0.744 | 10 |

7 | 270 | 220 | 110 | 0.989 | 10 |

8 | 270 | 190 | 110 | 0.858 | 10 |

9 | 370 | 350 | 110 | 1.241 | 10 |

10 | 370 | 450 | 110 | 1.723 | 10 |

11 | 370 | 250 | 120 | 0.833 | 10 |

12 | 370 | 250 | 130 | 0.828 | 10 |

13 | 370 | 250 | 140 | 0.827 | 10 |

The damage evolution results of cut blasting under different burdens are presented in Figure

Overall damage of prime cut blasting under different burdens: (a) scheme 1, (b) scheme 2, (c) scheme 3, (d) scheme 4, (e) scheme 5, and (f) scheme 6.

Compression damage of prime cut blasting under different burdens: (a) scheme 1, (b) scheme 2, (c) scheme 3, (d) scheme 4, (e) scheme 5, and (f) scheme 6.

Tension damage of prime cut blasting under different burdens: (a) scheme 1, (b) scheme 2, (c) scheme 3, (d) scheme 4, (e) scheme 5, and (f) scheme 6.

Further observation can be found in a large number of radial tensile cracks that appear in the direction without an empty hole, as shown in Figure

Figure

Overall damage of prime cut blasting under different diameters of the empty hole: (a) scheme 3, (b) scheme 7, (c) scheme 8, (d) scheme 5, (e) scheme 9, and (f) scheme 10.

Tension damage of prime cut blasting under different diameters of the empty hole: (a) scheme 3, (b) scheme 7, (c) scheme 8, (d) scheme 5, (e) scheme 9, and (f) scheme 10.

The comparisons of the damage zones under different prime cut hole diameters are shown in Figure

Overall damage of prime cut blasting under different diameters of the charge hole: (a) scheme 5, (b) scheme 11, (c) scheme 12, and (d) scheme 13.

Compression damage of prime cut blasting under different diameters of the charge hole: (a) scheme 5, (b) scheme 11, (c) scheme 12, and (d) scheme 13.

Tension damage of prime cut blasting under different diameters of the charge hole: (a) scheme 5, (b) scheme 11, (c) scheme 12, and (d) scheme 13.

According to the above analysis, there is a threshold of the burden, which can not only maximize the size of cut opening but also avoid incompletely damage of the burden rock. For the empty hole in cut blasting, it can transfer the blasting energy. If the diameter of the empty hole is small, most of the energy will be consumed in the creation of the long radial fractures. If the empty hole is large enough, more energy will be shifted in the direction of the empty hole and consumed in the creation of opening. That means that the larger the empty hole the more energy is used in the creation of the opening. However, considering the drilling cost, too large empty hole is waste and not necessary under a certain burden. Further, the increase of line charge density has a direct and obvious effect on rock failure and damage; meanwhile, more long radial cracks will be also created. Therefore, the relationship among the charge hole, burden, and empty hole is that the charge hole provides blasting energy; then, the empty hole transfers the blasting energy to break the burden rock and provides swelling space for rock fragments. In order to obtain a good effect of cut blasting, the relationship of cut parameters should be considered comprehensively.

The prime cut hole initiates to form an opening, which provides a free surface and swelling space for the subsequent cut holes in the process of cut blasting. Thus, appropriate prime cut hole parameters employed in a cut model can ensure the creation of opening. Too many radial cracks induced by improper parameters may influence the results of subsequent cut holes blasting and the stability of wall during one-step raise excavation. In this study, the parameters of

In engineering, there are four typical burn cut models for one-step raise excavation [

Four types of burn cut models with geometry and boundary conditions: (a) spiral cut, (b) diamond cut, (c) triangular prism cut, and (d) doliform cut.

The four typical numerical simulation models of burn cut are established, as shown in Figure

Figure

Cut blasting processes of four burn cut models: (a)–(d) spiral cut blasting process, (e)–(h) diamond cut blasting process, (i)–(l) triangular prism cut blasting process, and (m)–(p) doliform cut blasting process.

After 2 ms, the secondary cut holes are initiated in sequence, and the corresponding burden rock is completely broken in all numerical models. It can be clearly seen that the processes of cut openings were formed from the four cut models. The length of the radial fractures formed in the previous cut hole blasting greatly increases with the detonation of the next cut hole. Moreover, most of these cracks expanded outside of the cut openings may result in a negative effect for subsequent borehole initiation, even damage of the raise wall. A probable reason is that under the action of new hoop tension stress, the previous formed radial cracks are easy to continue expanding due to the low dynamic tension strength of rock mass.

The numerical results suggest that the number and layout of empty holes have a significant effect on the development of the damage zone. If a burn cut model, which has a few empty holes, is applied in one-step raise excavation, most of the energy will be consumed in creation of long radial cracks. Fortunately, the results will be opposite when the burn cut model has enough empty holes surrounding the prime cut hole. Considering the efficiency and damage control in the one-step raise excavation, the long radial crack should be avoided. So, in order to control the energy used for the creation of the opening, it is necessary to design more empty holes arranged around the prime cut hole in the burn cut model. However, considering the drilling technology and drilling cost, there are many boreholes in the section of triangular prism cut and doliform cut, so the workers’ drilling technology requirement is higher, and the drilling cost is also increased accordingly. Therefore, the choice of the burn cut mode is related to the depth of one-step raise excavation. For a deep raise or a blind raise, the burn cut model with more than three empty holes is optimal due to the high degree of constriction of the burden rock. For a raise with a depth of less than 10 m, the burn cut model with single or double empty holes can be adopted to reduce the cost, which is consistent with the research in Ref. [

In engineering, it is difficult to determine the cut parameters in one-step raise excavation. The objective of this study is to analyze the relationship between cut parameters and damage zones by using the numerical simulation method. Further, to achieve the optimal cut parameters, which are applied on four typical burn cut models to recommend a reasonable cut model by comparing the damage evolution and blasting energy utilization, the main conclusions can be drawn as follows:

The ideal burden length can maximize the use of blasting energy. When the burden is lower than the ideal value, only part of the energy is consumed in the creation of opening while the excess energy is wasted in the creation of long radial cracks. When the burden is greater than the ideal value, the burden rock may be incompletely damaged leading to the result that the opening cannot be formed

The empty hole as a free surface is effective in controlling the size and develop direction of the damage zone. With the increase of the empty hole diameter, more and more energy will be shift towards to the empty hole and consumed in the creation of opening. It demonstrates that the advantage of the large empty hole in burn cut

The linear charge density of the prime cut hole has a significant effect on damage evolution of cut blasting. The increase of the linear charge density means the increase of explosive energy, which will lead to the increase of the entire damage zone including burden damage and radial fractures. The optimal way to control most energy consumed in burden is that the diameter of the empty hole increases with the increase of the linear charge density

For spiral cut and diamond cut, there are only a few empty holes that are arranged in one side of the prime cut hole, and much blasting energy that is wasted results in that long radial fractures that are created in the other directions without an empty hole. For triangular prism cut and doliform cut, in which the layout of empty holes surrounds the prime cut hole, the corresponding burdens are damaged completely, and few radial fractures appear

All data, models, and code generated or used during the study can be found from the relevant references or appear in the submitted article.

The authors declare no conflict of interest.

The authors gratefully acknowledge the financial support of the China Postdoctoral Science Foundation (2019M662840), the National Key Research and Development Program of China (2016YFC0600706 and 2016YFC0600802) and Funded by the Open Research Fund Program of Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring (Central South University), Ministry of Education (2020YSJS13).