Frontiers in Computing and Intelligent Systems 
ISSN: 2832-6024 | Vol. 1, No. 1, 2022 

 

26 

Numerical simulation of charge blasting without 
coupling to air media 

Mingxiao Bai 1, * 

1 School of Civil Engineering, Henan Polytechnic University, Jiaozuo 454000, China; 

* Corresponding author: Mingxiao Bai (Email: 1409950099@qq.com).

 

Abstract: Blasting technology is one of the means commonly used in the excavation process of stone tunnels, in the blasting 

technology, it is mainly divided into glossy blasting and pre-cracking blasting. In the process of blasting, in order to prevent the 

excessive damage caused by explosive blasting, it is often used to blast by means of uncoupled charges. In this study, LS-DYNA 

was used to establish a three-dimensional model for numerical simulation of blasting, and the whole process of blasting of 

uncoupled charge was reproduced. By simulating the damage cloud map, the pressure on the pore wall and the vibration speed 

of the pore wall are analyzed and compared with the non-coupling coefficients k=1.5, 2, 2.5, and 3, which provides a theoretical 

basis for the calculation of the parameters of glossy blasting and pre-cracking blasting. 

Keywords: Uncoupling coefficient; Uncoupled charge; Blasting; LS-DYNA. 

 

1. Introduction 

Uncoupled charge is a special way to control blasting, 

through the uncoupled charge structure, that is, to maintain an 

appropriate distance between the explosive and the hole wall, 

thereby reducing the harm of the shock wave generated by the 

explosive explosion during the blasting process to the hole 

wall, eliminating the crushing area to achieve the effect of 

protecting the hole wall, making the glossy surface or pre-

crack smoother. 

Uncoupled charges are mainly used in glossy blasting and 

pre-cracking blasting. Holmes, the American, first applied 

uncoupled charging technology, and in the 1950s, he applied 

this technology to the construction of large hydropower 

stations, and the blasting effect exceeded expectations, and 

there was almost no hyper-explosion. Subsequently, the 

uncomplemented technology continued to evolve and 

improve. Through experimental research, Tengshan Bangjiu 

[1] found that the blasting effect is closely related to the 

distance between the charge hole and the space hole; 

Matsumoto. S et al. [2-3] analyze the stress wave propagation 

after blasting of an uncoupled charge by numerical simulation. 

In the early 1970s, uncomplemented charging technology was 

first applied in China. By the mid-1970s, uncoupled charge 

blasting technology was widely used in China's surface 

mining industry and achieved good results. 

In this paper, four uncoupling charge coefficients of k=1.5, 

k=2, k=2.5 and k=3 are considered, and the effects of blasting 

of different Uncoupling coefficients on rocks are explored by 

numerical simulation, which provides a theoretical basis for 

the calculation of glossy blasting and pre-cracking blasting 

parameters. 

2. Establishment of numerical model of 
blasting 

2.1. Model establishment 

Using ANSYS/LS-DYNA numerical simulation software 

to build a model, as shown in Figure 1, in order to study the 

impact of blasting with different coupling degrees on the 

surrounding rock, this paper considers four working 

conditions: condition 1 k=1.5, working condition 2 k=2, 

working condition 3 k=2.5, and condition 4 k=3. As shown in 

Figure 1, a quarter finite element model is established to 

improve computational efficiency. Cylindrical rock radius of 

1m, height of 0.1m, charge length of 0.5m, charging radius of 

0.045m, considering the interaction of rock, explosives and 

air 3 kinds of materials, the use of fluid-structure coupling 

algorithm, that is, rock using LaGrange algorithm, explosives 

and air using ALE algorithm, with the keyword * 

CONSTRAINED_LAGRANGE_IN_SOLID coupling the 

solid domain and fluid domain, the surrounding of the rock 

mass using non-reflective boundary condition to simulate the 

infinite rock area. 

 
Figure 1. Model diagram 

2.2. Material models and equations of state 

2.2.1. Explosive material model and equation of state 

parameters 

For explosive materials: The explosive constitutive 

*MAT_HIGH_EXPLOSIVE_BURN (material type 8) 

provided by the ANSYS/LS-DYNA software material library 

was used to simulate rock emulsified explosives No. 2, and 

the Jones-Wilkins-Lee equation of state (*EOS_JWL) was 

used to simulate the functional relationship between the 

pressure volume and energy of the detonation products during 

the explosion process, which has the following function 

equation: 

1 2

1 2

1 1R V R V E
P A e B e

RV R V V

  − −   
= − + − +   

     



 

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Where P is the explosion pressure; V is the relative volume; 

AJ, BJ, R1, R2 are equation of state parameters. The specific 

parameters are shown in Table 5: 

Table 1. Explosives material model and equation of state 
parameters 

ρ0 

Kg·m-3 

DJ 

m·s-1 

AJ 

GPa 

BJ 

GPa 
R1 R2   

E0 

J·m-3 

1050 4000 540.9 9.4 4.5 1.1 0.35 8×109 

2.2.2. Air material model and equation of state 

parameters 

For air materials: In LS-DYNA, air materials are typically 

defined by the keyword *MAT_NULL with * EOS_LIN 

EAR_POLYNOMIAL equation of state, which is: 

( )2 3 2

0 1 2 3 4 5 6P C C C C C C C E    = + + + + + +
 

Where: μ is the specific volume, which is the volume 

parameter used for calculation, μ=ρa/ρ0-1; ρa is the current 

moment density of the air; ρ0 is the initial moment density of 

air; E is the internal energy density. For specific parameters, 

see Table 2 

Table 2. Air material model and equation of state parameters 

ρ0 

Kg·m-3 
C0 C1 C2 C3 C4 C5 C6 

E 

KJ·m-3 
V 

1.293 0 0 0 0 0 0 0 235 1 

2.2.3. Model of rock materials 

At present, in dyna software, there are Mohr-Coulomb 

models and Drucker-Prager models for constitutive models of 

rock materials in geotechnical engineering. However, for rock 

materials, it is necessary to consider both strain rate effect and 

damage on rock strength and failure strain, and the 

JOHNSON_HOLMQUIST_CONCRETE damage 

constitutive model used in this paper is an ANSYS/LS-DYNA 

software, which is numbered 111. Proposed by Holmquist et 

al. [4] in 1993, the model takes into account simulations of 

concrete and rock at high strain rates and large deformations, 

model evolution equations and parameter references. 

(1) Strength model, which is described in terms of equal 

effect forces, considers the effects of strain, strength, strain 

rate, etc., and its expression is: 

( )* * *1 1 lnNA D BP C 
  

 = − + +   
    

(2) Damage model, which describes the degree of damage 

to the model, and its expression is: 

( ) 2* *

1

P P

D
D

D P T

  +
=

+


 
(3) Equation of state, the equation of state of the HJC model 

is used to describe the relationship between hydrostatic 

pressure and volumetric strain, and the whole process can be 

divided into three stages: elasticity, plasticity and compaction. 

Elastic Phase: 

eP k =
 

Plastic stage: 

( )crush crush crushP P K  = + −
 

Compaction Phase: 
2 3

1 2 3P K K K  = + +  

3. Simulation result analysis 

3.1. Injury 

As shown in Figure 2, a has a hole radius of 4.5cm, a 

explosive radius of 3cm, and a coupling coefficient k=1.5; b 

has a gunhole radius of 6cm, an explosive radius of 3cm, and 

a coupling coefficient k=2.0; c gunhole radius is 7.5cm, an 

explosive radius of 3cm, and a coupling coefficient of k=2.5; 

d gunhole radius is 9cm, an explosive radius is 3cm, and a 

coupling coefficient k=3.0; as can be seen from the figure, 

after blasting, the damage radius caused by working 

conditions a is the smallest; The maximum radius of damage 

caused by the rocks under working conditions d; It can be seen 

from this that, all other things being equal, the greater the 

coupling coefficient, the greater the damage to the rock after 

the explosives are blasted. 

 
(a)                     (b) 

 
(c)                    (d) 

Figure 2. Model of rock damage after blasting 

3.2. Hole wall pressure 

In order to study the effect of blasting with different 

coupling coefficients on the pressure caused, the monitoring 

point is selected at the same location and the pressure on the 

point under four different working conditions is analyzed, as 

shown in Figure 3. 

Figure a is the Uncoupling coefficient k= 1.5, the hole wall 

pressure after blasting, it can be seen from the figure that the 

maximum value is 0.245×109Pa; Figure b is the pressure of 

the hole wall after blasting when the Uncoupling coefficient 

k=2.0 is shown, and it can be seen from the figure that the 

maximum value is 0.154×109Pa; Figure c is the uncoupling 

coefficient k= 2.5, the hole wall pressure after blasting, it can 

be seen from the figure that the maximum value is 

0.154×109Pa; Figure d is the Uncoupling coefficient k= 3.0, 

the hole wall pressure after blasting, it can be seen from the 

figure that the maximum value is 0.152×109Pa; It can be seen 

that the larger the non-coupling coefficient, the smaller the 

pore wall pressure. 

   

 



 

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(a) K=1.5 

 
(b) K=2.0 

 
(c) K=2.5 

 
(d) K=3.0 

Figure 3. Pressure-time plot 

3.3. The vibration speed of the hole wall 

In order to study the impact of blasting with different 

coupling coefficients on the pressure caused, the vibration 

speed data of the monitoring points obtained in the limit of 

3.2 are extracted and sorted out, and the vibration speed of the 

measured points under four different working conditions is 

analyzed, as shown in Figure 4. 

Figure a is the Uncoupling coefficient k= 1.5, the vibration 

rate of the hole wall after blasting, it can be seen from the 

figure that the maximum value is 82m/s; Fig. b is the vibration 

speed of the hole wall after blasting when the uncoupling 

coefficient k=2.0 is shown, and it can be seen from the figure 

that the maximum value is 65 m/s; Figure c is the Uncoupling 

coefficient k= 2.5, the vibration speed of the hole wall after 

blasting, it can be seen from the figure that the maximum 

value is 57m/s; Figure d is the Uncoupling coefficient k= 3.0, 

the blast wall vibration speed after the blast, it can be seen 

from the figure that the maximum value is 53m/s; It can be 

seen that the larger the non-coupling coefficient, the smaller 

the vibration rate of the pore wall. 

 
(a) K=1.5 

 
(b) K=2.0 

 
(c) K=2.5 

 
(d) K=3.0 

Figure 4. Velocity-time plot 

4. Conclusion  

LS-DYNA was used to establish a three-dimensional 

numerical model with an Uncoupling coefficient of k=1.5, 

k=2, k=2.5, and k=3, and the numerical simulation was 

carried out, and the whole process of blasting was reproduced: 

under the same conditions, the greater the coupling coefficient, 

the greater the damage to the rock after the blasting of the 

explosives; The greater the coefficient of non-coupling, the 

less pressure the pore wall is subjected to. The larger the non-

coupling coefficient, the smaller the aperture wall vibration 

rate. It can be seen that the larger the non-coupling coefficient, 

the less harmful the shock wave generated by the explosive 

explosion to the hole wall, so the selection of a suitable non-

coupling coefficient in blasting can not only produce a 

smoother surface, but also control the degree of damage to the 

hole wall. 



 

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References 

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Coal Industry Press, 1979 

[2] Smith, P.D.(Cranfield Univ): Vismeg, P., Teo, LC.: Tingey, L. 
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International Jourmal of Impact Engineemg,v21, n6, Jul,1998, 
419-432. 

[3] Matsumoto, S.(Shock Wave/Condensed Matter Res.C., 
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[4] Johnson H G R . A Computational Constitutive Model for 
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