# Numerical Simulation Study on Parameter Optimization of Time Sequential Controlled Blasting

Authors: Meng He; Yehong Hu; Jin Chen; Jiazhao Zhang; Helong Li; Changgeng Cai
Journal: Shock and Vibration
 (2022)

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## Abstract

In order to reduce the damage of blasting to rock mass and improve the half-hole rate of presplitting blasting, the dynamic finite element analysis software ANSYS/LS-DYNA is used to simulate and analyze the action process of sequential controlled blasting. The effects of the detonation delay time of the postblasting hole and the hole spacing of the postblasting hole on the crack formation of the sequential controlled presplitting blasting are studied. The results show that when the blast hole with a diameter of 42 mm is used for sequential controlled presplitting blasting and the first blast hole pitch is 60 cm, the reasonable detonation delay time is 80∼120μs. When the detonation delay time is 80 μs, the reasonable postblast hole spacing is 60 cm. Field tests show that when reasonable optimized blasting parameters are used, presplit blasting with sequential control can reduce drilling workload and explosive consumption. The sequential controlled presplitting blasting not only increases the hole spacing but also plays a better role in protecting the surrounding rock.


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## Body

## 1. Introduction

Blasting is widely used in mine mining, tunnel excavation, and other projects because of its high efficiency, economic characteristics, and strong adaptability to geology [1, 2]. For the project that needs to accurately control the blasting excavation surface, the crack formation and forming effect of presplitting blasting construction directly affect the project progress and project cost. In order to ensure good construction quality and reduce blasting costs, it is necessary to find a feasible directional control blasting to improve it [3, 4].The application of presplitting blasting and smooth blasting in actual blasting engineering has obvious advantages, but they also have some shortcomings [5]. The most important of which is that they generally use small holes of less than 100 mm in diameter. According to experience, the spacing of presplit holes or smooth holes is generally 8–12 times the blast hole diameter. When the hole diameter is 100 mm, the distance between presplit holes or smooth holes is 0.8～1.2 m, while the distance between ordinary hole deep blasting holes is greater than 2.5 m. It can be seen that the blast hole spacing of presplit blasting and smooth blasting is much smaller than that of ordinary blasting. Under the same engineering volume, small blast hole spacing means a large number of holes, which will inevitably increase drilling costs. However, drilling costs account for about 50–70% of the entire blasting cost, which will naturally increase the blasting cost. In order to reduce the blasting cost and save the engineering cost, it is an inevitable measure to increase the spacing between the presplitting hole and the smooth face. The current method of increasing the distance between the presplit blast hole and the smooth hole is mainly achieved by controlling the fracture blasting method [6–8].Sequential controlled presplitting blasting is a controlled fracture blasting method based on the empty hole effect [9–11]. Compared with the conventional presplitting blasting method, it can not only reduce the blasting cost but also ensure a good blasting effect. Due to the void effect, the explosive stress wave of the first blast hole produces a stress concentration effect on the wall of the later blast hole, which makes the wall of the latter blast hole produce a prefabricated radial crack. The crack produced by blasting provides sufficient propagation conditions for the fracture of the latter initiation hole. From the action mechanism of presplitting blasting under sequential control, it can be seen that the hole distance of the post blasting hole has a significant influence on its blasting effect. Therefore, it is of great significance to study the hole spacing of postblasting hole for the sequential controlled blasting method. At present, there is no recognized calculation method for the determination of the postblast hole distance at home and abroad, and the final determination is mainly based on the data obtained from the field test and numerical simulation [12–14]. Another key technical parameter in sequential control fracture blasting is the detonation delay time. In order to make the first and second blast holes interact and achieve the desired blasting effect, it is necessary to determine a reasonable timing control delay time [15]. The time sequence control delay time should also meet another requirement, that is, when the second blast hole detonates, the dynamic stress field generated by the first blast hole has not disappeared.In this paper, the smooth blasting of the vertical surface in the excavation of foundation pits was used as a benchmark, the sequential controlled smooth blasting technology with a small aperture was studied. By establishing different finite element analysis models, calculating the stress field distribution rules in various models, comparing the stress values of key parts, the effect of detonation delay time and postblast hole spacing on the blasting effect was studied.


## 2. Establishment of Finite Element Model

### 2.1. Geometric Model

The size of the model was 120 cm × 120 cm. The diameter of the blast hole charge was 14 mm, the hole depth was 100 cm, and the charge length was 70 cm. The bottom of the hole was used for detonation. According to the main blast hole network parameters of the previous on-site presplitting blasting construction, combined with the actual construction of foundation pit blasting and excavation, the blast hole diameter was determined to be 42 mm in the numerical simulation study. The first blasting hole pitch is 40 cm, and the latter blasting hole pitch is 40, 60, and 80 cm, respectively. According to the action mechanism of sequential control presplitting blasting, 1 cycle section (2 first blast holes and 2 postblast holes) is selected to establish a numerical simulation model for analysis. Due to the symmetry of the model, in order to reduce computing resources, half of the model was established for calculation and analysis by using the common node method. The boundary conditions of the model were defined as follows: free boundary conditions were applied to the front boundary, symmetric boundary conditions were applied to the profile, and unconditional reflection boundary conditions were applied to other surfaces in the simulation. The established numerical analysis model is shown in Figure1.Figure 1
Numerical analysis model in ANSYS/LS-DYNA.


### 2.2. Simulation Materials and Parameters

The Solid164 volume element in ANSYS/LS-DYLA software was selected to establish a numerical calculation model. The numerical calculation model mainly involved three materials: rock, explosive, and air, among which the Lagrange algorithm was used for rock, and the ALE algorithm was used for explosives and air. Since the blasting process is simulated, when selecting them in the ANSYS/LS-DYNA material library, the characteristics of the corresponding material that meets the large deformation should be considered. The rock material model used the∗MAT_PLASTIC_KINEMATIC model in the ANSYS/LS-DYNA program, and the specific parameters are shown in Table 1. The explosive material model was described by the ∗MAT_HIGH_EXPLOSIVE_BURN model, and the corresponding JWL equation of state was used to simulate the explosive load. The explosive material parameters are shown in Table 2. Air was defined as ∗MAT_NULL material model, and the parameters of air material are shown in Table 3. The rock parameters used in the numerical simulation were mainly obtained from the engineering geological data in engineering site as well as the laboratory test results.Table 1
Rock material parameters.
Density/kg·m−3Elastic modulus/GPaPoisson’s ratioYield Strength/MPaTangent modulus/GPa279037.80.21121.414.2Table 2
Explosive material parameters.
JWL state equation parameters [16]Density/g·cm−3Detonation velocity/km·s−1Burst pressure/GPaA/GPaB/GPaR1R2ωE0/GPa212.60.1794.11.00.164.231.224.654.5Table 3
Air material parameters.
Density/g·m−3C0C1C2C3C4C5C6V0E1.29 × 10300000.40.4012.5 × 10−6


### 2.3. Rock Failure Criterion and Simulation Conditions

In the process of blasting simulation with ANSYS/LS-DYNA, the failure criterion of the rock depends on the nature of the rock mass and the actual force state, and the fracture area is mainly the result of tensile failure. Therefore, in the analysis process of numerical simulation results, the stress field distribution law and blasting fracture characteristics in the blasting process are mainly analyzed by the magnitude of the tensile stress value. For the value of dynamic tensile strength of rock mass, due to the lack of corresponding theoretical and experimental research, it is difficult to accurately give its precise value. The dynamic tensile strength of the rock mass is taken as 3 times the static tensile strength of the rock. On-site geological data shows that the static tensile strength of the rock is 6.86 MPa, so the dynamic tensile strength of the rock mass is taken as 20.6 MPa. The simulation conditions of sequential controlled presplitting blasting are shown in Table4.Table 4
Air material parameters.
Condition numberPostblast hole spacing/cmDetonation delay time/μs1408026038046005406807120


## 2.1. Geometric Model

The size of the model was 120 cm × 120 cm. The diameter of the blast hole charge was 14 mm, the hole depth was 100 cm, and the charge length was 70 cm. The bottom of the hole was used for detonation. According to the main blast hole network parameters of the previous on-site presplitting blasting construction, combined with the actual construction of foundation pit blasting and excavation, the blast hole diameter was determined to be 42 mm in the numerical simulation study. The first blasting hole pitch is 40 cm, and the latter blasting hole pitch is 40, 60, and 80 cm, respectively. According to the action mechanism of sequential control presplitting blasting, 1 cycle section (2 first blast holes and 2 postblast holes) is selected to establish a numerical simulation model for analysis. Due to the symmetry of the model, in order to reduce computing resources, half of the model was established for calculation and analysis by using the common node method. The boundary conditions of the model were defined as follows: free boundary conditions were applied to the front boundary, symmetric boundary conditions were applied to the profile, and unconditional reflection boundary conditions were applied to other surfaces in the simulation. The established numerical analysis model is shown in Figure1.Figure 1
Numerical analysis model in ANSYS/LS-DYNA.


## 2.2. Simulation Materials and Parameters

The Solid164 volume element in ANSYS/LS-DYLA software was selected to establish a numerical calculation model. The numerical calculation model mainly involved three materials: rock, explosive, and air, among which the Lagrange algorithm was used for rock, and the ALE algorithm was used for explosives and air. Since the blasting process is simulated, when selecting them in the ANSYS/LS-DYNA material library, the characteristics of the corresponding material that meets the large deformation should be considered. The rock material model used the∗MAT_PLASTIC_KINEMATIC model in the ANSYS/LS-DYNA program, and the specific parameters are shown in Table 1. The explosive material model was described by the ∗MAT_HIGH_EXPLOSIVE_BURN model, and the corresponding JWL equation of state was used to simulate the explosive load. The explosive material parameters are shown in Table 2. Air was defined as ∗MAT_NULL material model, and the parameters of air material are shown in Table 3. The rock parameters used in the numerical simulation were mainly obtained from the engineering geological data in engineering site as well as the laboratory test results.Table 1
Rock material parameters.
Density/kg·m−3Elastic modulus/GPaPoisson’s ratioYield Strength/MPaTangent modulus/GPa279037.80.21121.414.2Table 2
Explosive material parameters.
JWL state equation parameters [16]Density/g·cm−3Detonation velocity/km·s−1Burst pressure/GPaA/GPaB/GPaR1R2ωE0/GPa212.60.1794.11.00.164.231.224.654.5Table 3
Air material parameters.
Density/g·m−3C0C1C2C3C4C5C6V0E1.29 × 10300000.40.4012.5 × 10−6


## 2.3. Rock Failure Criterion and Simulation Conditions

In the process of blasting simulation with ANSYS/LS-DYNA, the failure criterion of the rock depends on the nature of the rock mass and the actual force state, and the fracture area is mainly the result of tensile failure. Therefore, in the analysis process of numerical simulation results, the stress field distribution law and blasting fracture characteristics in the blasting process are mainly analyzed by the magnitude of the tensile stress value. For the value of dynamic tensile strength of rock mass, due to the lack of corresponding theoretical and experimental research, it is difficult to accurately give its precise value. The dynamic tensile strength of the rock mass is taken as 3 times the static tensile strength of the rock. On-site geological data shows that the static tensile strength of the rock is 6.86 MPa, so the dynamic tensile strength of the rock mass is taken as 20.6 MPa. The simulation conditions of sequential controlled presplitting blasting are shown in Table4.Table 4
Air material parameters.
Condition numberPostblast hole spacing/cmDetonation delay time/μs1408026038046005406807120


## 3. Optimization of Postblast Hole Spacing

The purpose of sequential control blasting is to increase the hole distance, reduce the drilling volume, and reduce the blasting cost. It mainly relies on the void effect to form prefabricated radial cracks on the hole wall of the rear blast hole, increasing the distance between the two rear blast holes. Therefore, the purpose of the optimization study of sequential controlled smooth blasting in this paper is to select an optimal postblast hole spacing and guide the site construction to use sequential controlled blasting for slope excavation tests.


### 3.1. Stress Field Analysis

According to the analysis of the calculation results, it is found that the stress range between the postblasting holes during the entire blasting process can be clearly and intuitively displayed at 247μs and 502 μs and has obvious comparability. Therefore, the stress diagrams of each model at 247 μs and 502 μs are given for analysis, as shown in Figures 2∼4.Figure 2
Nephogram of the first principal stress with a distance of 40 cm from the postblast hole (unit: 1011 Pa): (a) 247 μs and (b) 502 μs.
(a)(b)Figure 3
Nephogram of the first principal stress with a distance of 60 cm from the postblast hole (unit: 1011 Pa): (a) 247 μs and (b) 502 μs.
(a)(b)Figure 4
Nephogram of the first principal stress with a distance of 80 cm from the postblast hole (unit: 1011 Pa): (a) 247 μs and (b) 502 μs.
(a)(b)From Figures2∼4, it can be seen that after the explosive is detonated, the explosion stress wave generated by it will expand from the hole wall to the surrounding area as a cylindrical wave. As the grains move upward in this fixed area, a maximum stress range is finally formed. From the stress nephogram, it can be seen that the stress wave generated by the two postblast holes mainly acts on the inner side of the blast hole (between the two postblast holes). The stress action range generated by the two postblast holes will be superimposed between the two blast holes to form a tensile stress action area.The comparative analysis of the stress nephograms of four different postblast hole pitches shows that the postblast hole spacing has a very significant influence on the stress change between two postblast holes. With the increase in the distance between the postexplosion hole, the two postblast hole detonation produces a gradual reduction in the range of stress effects. When the hole spacing increases to 100 cm, the tensile stress action zone between the two postblasting holes is not connected. It shows that the effect of the blasting stress wave on the rock mass does not exceed the dynamic tensile strength of the rock mass, and the rock mass between the two blast holes cannot form a completely penetrating crack.


### 3.2. Displacement Field Analysis

The displacement nephograms of different postblast hole pitch models at 247μs and 502 μs are shown in Figures 5∼7. It can be seen from the figure that the three models have formed a large displacement area near the blast hole. With the increase of the distance between the postblast holes, the displacement between the two postblast holes gradually decreases. When the distance between the postblast holes is 40 cm and 60 cm, the displacement change area between the two postblast holes is connected, but when the distance between the postblast holes is 80 cm, the displacement change area between the two postblast holes is separated. It shows that the force of the blasting stress wave on the central rock mass is weak, and it is difficult to form through cracks.Figure 5
Nephogram of displacement with a distance of 40 cm from the postblast hole (unit: m): (a) 247μs and (b) 502 μs.
(a)(b)Figure 6
Nephogram of displacement with a distance of 60 cm from the postblast hole (unit: m): (a) 247μs and (b) 502 μs.
(a)(b)Figure 7
Nephogram of displacement with a distance of 80 cm from the postblast hole (unit: m): (a) 247μs and (b) 502 μs.
(a)(b)


### 3.3. Analysis of Maximum Principal Stress

In order to further analyze and judge the smooth blasting effect between the two blast holes, a monitoring line is arranged on the center line perpendicular to the line connecting the two postblast holes. Eight measuring points are arranged on the monitoring line, the first measuring point is at the bottom of the model, and the eighth measuring point is at the free surface at the bottom of the model. The time history curve of the first principal stress of a series of elements on the monitoring line was recorded and extracted, and the maximum first principal stress value of each element was read. The tensile yield criterion is used to judge the failure of the element, and the blasting effect of sequential control smooth blasting is observed according to the results. Since the calculation model has a certain symmetry, it can be known that the forces on the elements located on both sides of the center line are the same. In the case of different postblast hole distances, the change rule of the maximum first principal stress of each monitoring unit from the bottom to the top of the blast hole is shown in Figure8.Figure 8
Variation law of maximum stress of monitoring unit in each model.Under different postblast hole spacing, with the increase of postblast hole spacing, the maximum first principal stress of the monitoring unit in each model shows an overall decreasing trend. The postblasting hole spacing is small, and the overall maximum stress value is large; the postblasting hole spacing is large, and the overall maximum stress value is small. This shows that with the increase of the hole spacing, the damage effect of blasting on the rock is weakening. When the postblast hole distance is 60 cm, the maximum tensile stress of each monitoring unit on the center line is greater than the rock’s dynamic tensile strength value of 20.6 MPa. When the postblast hole distance is 80 cm, the maximum tensile stress values for some units appear to be less than 20.6 MPa. The purpose of smooth blasting is not only to make the peak stress between the two holes greater than the tensile strength of the rock mass, so that the middle rock can be destroyed to form a flat reserved surface, but also to minimize the peak pressure to reduce its damage to the surrounding rock. In order to achieve the best smooth blasting effect, the optimal hole spacing of blasting holes after sequential control smooth blasting can be 60 cm.


## 3.1. Stress Field Analysis

According to the analysis of the calculation results, it is found that the stress range between the postblasting holes during the entire blasting process can be clearly and intuitively displayed at 247μs and 502 μs and has obvious comparability. Therefore, the stress diagrams of each model at 247 μs and 502 μs are given for analysis, as shown in Figures 2∼4.Figure 2
Nephogram of the first principal stress with a distance of 40 cm from the postblast hole (unit: 1011 Pa): (a) 247 μs and (b) 502 μs.
(a)(b)Figure 3
Nephogram of the first principal stress with a distance of 60 cm from the postblast hole (unit: 1011 Pa): (a) 247 μs and (b) 502 μs.
(a)(b)Figure 4
Nephogram of the first principal stress with a distance of 80 cm from the postblast hole (unit: 1011 Pa): (a) 247 μs and (b) 502 μs.
(a)(b)From Figures2∼4, it can be seen that after the explosive is detonated, the explosion stress wave generated by it will expand from the hole wall to the surrounding area as a cylindrical wave. As the grains move upward in this fixed area, a maximum stress range is finally formed. From the stress nephogram, it can be seen that the stress wave generated by the two postblast holes mainly acts on the inner side of the blast hole (between the two postblast holes). The stress action range generated by the two postblast holes will be superimposed between the two blast holes to form a tensile stress action area.The comparative analysis of the stress nephograms of four different postblast hole pitches shows that the postblast hole spacing has a very significant influence on the stress change between two postblast holes. With the increase in the distance between the postexplosion hole, the two postblast hole detonation produces a gradual reduction in the range of stress effects. When the hole spacing increases to 100 cm, the tensile stress action zone between the two postblasting holes is not connected. It shows that the effect of the blasting stress wave on the rock mass does not exceed the dynamic tensile strength of the rock mass, and the rock mass between the two blast holes cannot form a completely penetrating crack.


## 3.2. Displacement Field Analysis

The displacement nephograms of different postblast hole pitch models at 247μs and 502 μs are shown in Figures 5∼7. It can be seen from the figure that the three models have formed a large displacement area near the blast hole. With the increase of the distance between the postblast holes, the displacement between the two postblast holes gradually decreases. When the distance between the postblast holes is 40 cm and 60 cm, the displacement change area between the two postblast holes is connected, but when the distance between the postblast holes is 80 cm, the displacement change area between the two postblast holes is separated. It shows that the force of the blasting stress wave on the central rock mass is weak, and it is difficult to form through cracks.Figure 5
Nephogram of displacement with a distance of 40 cm from the postblast hole (unit: m): (a) 247μs and (b) 502 μs.
(a)(b)Figure 6
Nephogram of displacement with a distance of 60 cm from the postblast hole (unit: m): (a) 247μs and (b) 502 μs.
(a)(b)Figure 7
Nephogram of displacement with a distance of 80 cm from the postblast hole (unit: m): (a) 247μs and (b) 502 μs.
(a)(b)


## 3.3. Analysis of Maximum Principal Stress

In order to further analyze and judge the smooth blasting effect between the two blast holes, a monitoring line is arranged on the center line perpendicular to the line connecting the two postblast holes. Eight measuring points are arranged on the monitoring line, the first measuring point is at the bottom of the model, and the eighth measuring point is at the free surface at the bottom of the model. The time history curve of the first principal stress of a series of elements on the monitoring line was recorded and extracted, and the maximum first principal stress value of each element was read. The tensile yield criterion is used to judge the failure of the element, and the blasting effect of sequential control smooth blasting is observed according to the results. Since the calculation model has a certain symmetry, it can be known that the forces on the elements located on both sides of the center line are the same. In the case of different postblast hole distances, the change rule of the maximum first principal stress of each monitoring unit from the bottom to the top of the blast hole is shown in Figure8.Figure 8
Variation law of maximum stress of monitoring unit in each model.Under different postblast hole spacing, with the increase of postblast hole spacing, the maximum first principal stress of the monitoring unit in each model shows an overall decreasing trend. The postblasting hole spacing is small, and the overall maximum stress value is large; the postblasting hole spacing is large, and the overall maximum stress value is small. This shows that with the increase of the hole spacing, the damage effect of blasting on the rock is weakening. When the postblast hole distance is 60 cm, the maximum tensile stress of each monitoring unit on the center line is greater than the rock’s dynamic tensile strength value of 20.6 MPa. When the postblast hole distance is 80 cm, the maximum tensile stress values for some units appear to be less than 20.6 MPa. The purpose of smooth blasting is not only to make the peak stress between the two holes greater than the tensile strength of the rock mass, so that the middle rock can be destroyed to form a flat reserved surface, but also to minimize the peak pressure to reduce its damage to the surrounding rock. In order to achieve the best smooth blasting effect, the optimal hole spacing of blasting holes after sequential control smooth blasting can be 60 cm.


## 4. Optimization of Detonation Delay Time

The key technology of sequential controlled blasting is to prefabricate the radial crack on the postblasting hole by using the delay time difference of initiation and combined with the stress concentration effect of the empty hole. The detonation delay time between the first blast hole and the latter blast hole is too short. Before the latter blast hole is detonated, the stress wave generated by the first blast hole cannot propagate to the vicinity of the later blast hole, and the void effect cannot be produced. If the time is too long, the stress wave generated by the first blast hole has attenuated and cannot be superimposed with the stress wave generated by the later blast hole. Therefore, the length of the initiation delay will have a serious impact on the blasting effect of sequential control smooth blasting.


### 4.1. Stress Field Analysis

According to the analysis of the calculation results, it is found that the stress range between the postblasting holes in the whole blasting process can be clearly and intuitively displayed at 258μs and 502 μs, and it has obvious comparability. Figures 9∼12 show the stress diagrams of each model at 258 μs and 502 μs. It can be seen from the figure that as the delay time increases, the maximum tensile stress generally increases first and then decreases. In addition, it can also be seen that in the delay time used in all simulations, when the time is 80 μs, the maximum tensile stress value of each monitoring unit is relatively large, which will be more conducive to the formation of precracks.Figure 9
The first principal stress nephogram with the detonation delay (T) = 0 μs (unit: 1011 Pa): (a) 258 μs and (b) 502 μs.
(a)(b)Figure 10
The first principal stress nephogram with the detonation delay (T) = 40 μs (unit: 1011 Pa): (a) 258 μs and (b) 502 μs.
(a)(b)Figure 11
The first principal stress nephogram with the detonation delay (T) = 80 μs (unit: 1011 Pa): (a) 258 μs and (b) 502 μs.
(a)(b)Figure 12
The first principal stress nephogram with the detonation delay (T) = 120 μs (unit: 1011 Pa): (a) 258 μs and (b) 502 μs.
(a)(b)


### 4.2. Analysis of Maximum Principal Stress

The time history curve of the first principal stress at the top of the hole under the four detonation delay times is shown in Figure13. It can be seen that the waveform of the maximum principal stress is different under different initiation delay time. When the detonation delay time is 0 μs and 120 μs, the waveform of the maximum principal stress is a double peak type. When the detonation delay time is 40 μs and 80 μs, the waveform of the maximum principal stress is single peak type. The variation law of the maximum first principal stress of each monitoring unit from the bottom to the top of the blast hole is shown in Figure 14. It can be seen that as the detonation delay time increases, the maximum first principal stress curve generally increases first and then decreases. When the initiation delay time is 40 μs, the maximum first principal stress of each monitoring unit is relatively reduced. The main reason is that the stress wave of the first blasting hole has not been transmitted to the hole wall of the second blasting hole when the explosive of the second blasting hole is detonated. When the initiation delay time is 80 μs and 120 μs, the maximum first principal stress of each element increases obviously. When the delay time is 80 μs, the overall maximum principal stress of each monitoring unit is relatively maximum. This is because the stress wave generated by the first blasting hole reaches the hole wall of the latter blasting hole before the initiation of the latter blasting hole and forms the empty hole effect, which achieves the desired effect of sequential controlled blasting. When the initiation delay time is 120 μs, the explosion stress wave generated by the first hole decays rapidly with time, and the superposition effect of the stress wave generated by the first hole and the second hole weakens.Figure 13
Time history curves of maximum principal stress under different initiation delay time: (a) 0μs, (b) 40 μs, (c) 80 μs, and (d) 120 μs.
(a)(b)(c)(d)Figure 14
Variation law of maximum stress of monitoring unit in each model.


## 4.1. Stress Field Analysis

According to the analysis of the calculation results, it is found that the stress range between the postblasting holes in the whole blasting process can be clearly and intuitively displayed at 258μs and 502 μs, and it has obvious comparability. Figures 9∼12 show the stress diagrams of each model at 258 μs and 502 μs. It can be seen from the figure that as the delay time increases, the maximum tensile stress generally increases first and then decreases. In addition, it can also be seen that in the delay time used in all simulations, when the time is 80 μs, the maximum tensile stress value of each monitoring unit is relatively large, which will be more conducive to the formation of precracks.Figure 9
The first principal stress nephogram with the detonation delay (T) = 0 μs (unit: 1011 Pa): (a) 258 μs and (b) 502 μs.
(a)(b)Figure 10
The first principal stress nephogram with the detonation delay (T) = 40 μs (unit: 1011 Pa): (a) 258 μs and (b) 502 μs.
(a)(b)Figure 11
The first principal stress nephogram with the detonation delay (T) = 80 μs (unit: 1011 Pa): (a) 258 μs and (b) 502 μs.
(a)(b)Figure 12
The first principal stress nephogram with the detonation delay (T) = 120 μs (unit: 1011 Pa): (a) 258 μs and (b) 502 μs.
(a)(b)


## 4.2. Analysis of Maximum Principal Stress

The time history curve of the first principal stress at the top of the hole under the four detonation delay times is shown in Figure13. It can be seen that the waveform of the maximum principal stress is different under different initiation delay time. When the detonation delay time is 0 μs and 120 μs, the waveform of the maximum principal stress is a double peak type. When the detonation delay time is 40 μs and 80 μs, the waveform of the maximum principal stress is single peak type. The variation law of the maximum first principal stress of each monitoring unit from the bottom to the top of the blast hole is shown in Figure 14. It can be seen that as the detonation delay time increases, the maximum first principal stress curve generally increases first and then decreases. When the initiation delay time is 40 μs, the maximum first principal stress of each monitoring unit is relatively reduced. The main reason is that the stress wave of the first blasting hole has not been transmitted to the hole wall of the second blasting hole when the explosive of the second blasting hole is detonated. When the initiation delay time is 80 μs and 120 μs, the maximum first principal stress of each element increases obviously. When the delay time is 80 μs, the overall maximum principal stress of each monitoring unit is relatively maximum. This is because the stress wave generated by the first blasting hole reaches the hole wall of the latter blasting hole before the initiation of the latter blasting hole and forms the empty hole effect, which achieves the desired effect of sequential controlled blasting. When the initiation delay time is 120 μs, the explosion stress wave generated by the first hole decays rapidly with time, and the superposition effect of the stress wave generated by the first hole and the second hole weakens.Figure 13
Time history curves of maximum principal stress under different initiation delay time: (a) 0μs, (b) 40 μs, (c) 80 μs, and (d) 120 μs.
(a)(b)(c)(d)Figure 14
Variation law of maximum stress of monitoring unit in each model.


## 5. Engineering Application of Optimized Parameters

In order to verify the practicability of the optimized parameters of presplitting blasting, the field test of presplitting blasting of permanent slope was carried out. The blast hole diameter is 42 mm, the hole spacing of the first blast hole is 40 cm, and the hole spacing of the second blast hole is 60 cm. The initiation delay time of the first blast hole and second blast hole is 80μs. The inclination of the blast hole is the same as the slope of the designed slope, which is 80°. The line charge density is 850 g/m, and the bottom is 1 m for reinforced charge. A total of 10 presplit holes were set in the test. Figure 15 shows the residual blasting holes on the rock surface in presplit blasting test. From Figure 15, it can be seen that there are 8 remaining semipores on the rock surface, with a semiporosity rate of 80%. It can be seen that after using the optimized blasting parameters for presplitting blasting, in the complete section of the rock, the semiporous rate of permanent slope blasting is controlled above 80%. The blasting wave generated after an explosive explosion acts on the blast hole wall. The blasting wave propagates continuously and gradually attenuates into a stress wave. Under the action of stress wave, the rock mass around the blasting hole will produce compressive stress and compressive deformation in the radial direction and produce tensile stress and tensile deformation in the tangential direction. Because the tensile strength of the rock is much smaller than its compressive strength, when the tangential tensile stress is greater than the tensile strength of the rock, the rock will be broken, and radial cracks perpendicular to the crushing area are formed near the blast hole. The purpose of controlled blasting is to reduce the damage of explosion impact pressure to the protected surrounding rock and ensure the engineering stability of the protected surrounding rock. The presplitting blasting effect of the optimized parameters can be accepted by the construction personnel.Figure 15
Photograph of residual blasting hole on the rock surface in presplit blasting test.


## 6. Conclusions

The dynamic finite element analysis software ANSYS/LS-DYNA is used to simulate and analyze the action process of sequential controlled blasting. The parameter optimization of initiation delay time and postblasting hole spacing is studied, and the reasonable blasting parameters are selected. The main conclusions are summarized as follows:(1)
Through the simulation study of sequential controlled blasting, it is found that after the explosive in the charge hole is detonated, the maximum value of the first principal stress (principal tensile stress) appears on the wall of the blast hole. It can be considered that the crack starts from the hole wall. In the process of the explosion stress wave of the first blast hole, the wall of the latter blast hole will have obvious stress concentration. The void effect can produce a certain length of crack before the postblasting initiation(2)
With the increase of the detonation delay time, the maximum first principal stress of the rock elements on the center line of the two postblast holes showed a trend of first increasing and then decreasing. With the increase of postblasting hole spacing, the destructive effect of blasting on rock is weakening. The effect of smooth blasting controlled by time sequence becomes worse with the increase of postblasting hole spacing. In order to achieve the best smooth blasting effect, the optimal hole spacing of blasting holes after sequential control smooth blasting can be 60 cm, and the initiation delay time can be 80μs.(3)
The field test of presplitting blasting of permanent slope verifies the practicability of blasting parameters. Through the field presplitting blasting test, it can be known that in the complete section of the rock, using the proposed line charge density and net requirements, the half-hole rate of permanent slope blast holes can be controlled above 80%. The sequential controlled presplitting blasting not only increases the hole spacing but also plays a better role in protecting the surrounding rock.



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*Source: 8728953-2022-02-23.xml*