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This paper attempts to calculate the exact initial shock pressure of borehole wall induced by the blasting with axially decoupled charge. For this purpose, Starfield superposition was introduced considering the attenuation and superposition of blasting pressure, and the theoretical solution of initial borehole wall pressure was obtained for the upper and middle air-decked charging structures. Then, the explosive pressure field around the borehole was measured by cement mortar models and a dynamic pressure test system, and the pressures at multiple measuring points were simulated with numerical models established by ANSYS/LS-DYNA. The results show that the deviations between simulated and theoretical pressures are smaller than 10%, indicating the reliability of the theoretical formula derived by Starfield superposition. For the upper air-decked charging structure, the initial shock pressure of the charging section followed a convex distribution, with the peak value near the charge centre. With the increase in the distance from the charging section, the borehole wall shock pressure in the air gap underwent a sharp decline initially before reaching a relatively constant level. The minimum pressure was observed at the hole collar. For the middle air-decked charging structure, the pressures at both ends of the charging section obeyed a convex distribution, with the peak value near the charge centre. Finally, the author optimized air-decked charging structure of periphery boreholes within Grade III surrounding rocks of Banjie tunnel, China, and proved the enhancement effect of the theoretical findings on smooth blasting. The research findings provide valuable references to the theoretical and experimental calculation of air column length and other key parameters of air-deck blasting and shed new light on the charging structure determination of smooth blasting and blasting vibration control for the excavation of large-section, deep mining roadways.

During the excavation of deep roadway or tunnel under high crustal pressure, the stability of the surrounding rock is dependent on the effect of smooth blasting, which itself hinges on the selection of axial decoupling coefficient. Concerning the close ties between the coefficient, the air gap, and the initial shock pressure of the borehole wall, below is a brief review of the existing studies on mine blasting, especially air-deck blasting, that involves these three elements.

In previous research, the initial shock pressure of borehole wall with air-decked charge is considered as 8~11 times the quasi-static pressure of the detonation gas [

To disclose the mechanism of air-deck blasting, Kabwe [

Yang et al. [

Over the years, much research has been done on the pressure distribution of borehole wall. Despite the lack of direct measuring methods, the borehole wall pressure has been estimated with various empirical formulas or detonation theories [

With the development of computer technology and intelligent testing, a series of new approaches have been introduced to reveal the dynamic effect of rock blasting, e.g., numerical simulation and model test. With the aid of LS-DYNA and FLAC3D, Jiang et al. [

Focusing on directional pressure-relief blasting, Xiao et al. [

The above studies open a new direction for quantifying the distribution of initial shock pressure in borehole wall. Considering air-deck blasting, Yang et al. [

Under coupled/decoupled charge, Ling [

This paper aims to select a proper axial decoupling coefficient for air-deck blasting. To this end, it is necessary to investigate the air gap and the initial shock pressure of the borehole wall under axial decoupled charge. Here, the Grade III surrounding rock of Banjie tunnel, a 4,806m-long deep-buried tunnel, is taken as the object. The tunnel is one of the three main tunnels in Yongren-Guangdong section of Chengdu-Kunming railway. In the tunnel, the surrounding rock masses are mostly Grade III~V sandstone and sandy mudstone. The tunnel segments through Grades III, IV, and V rocks are, respectively, 4,115m, 530m, and 161m in length. Thus, the object tunnel segment accounts for 85.6% of the total length of Banjie tunnel. The physical-mechanical parameters of Grade III surrounding rock are listed in Table

Physical-mechanical parameters of Grade III surrounding rock.

Density(kg/m^{3}) | Compressive strength(MPa) | Tensile strength (MPa) | Shear strength (MPa) | Longitudinal wave velocity (m/s) | Poisson ratio |
---|---|---|---|---|---|

2700 | 75 | 5.6 | 23.3 | 3350 | 0.23 |

The previous smooth blasting of Grade III surrounding rock was carried out in two steps with the following parameters: the total sectional area=116.02 m2, the excavation height= 5.81m (upper stage) and 5.52m (lower stage), and the cyclic advancement=3~3.2m. In the upper stage, the construction parameters are as follows: borehole distance= 50cm (periphery holes) and 80cm (auxiliary holes); and borehole depth=3.8m (periphery holes) and 4m (auxiliary holes). For the five-stage double horizontal wedge cutting, the vertical hole is 4m in depth. The density and detonation velocity of 2# emulsion explosive are 1,300kg/m3 and 3,200m/s, respectively. Due to the high detonator cost and complex process, the periphery holes were charged continuously at the bottom (hereinafter referred to as the continuous bottom charging).

The above blasting structure has some problems that led to an unsuccessful tunnelling. After the smooth blasting on the upper stage, the maximum overbreak was as high as 0.4m near the working face (hole bottom) of the hance, and the maximum underbreak near lining (hole collar) stood at 0.25m. At the vault, the postblast outline exhibited as a large flat plate with severe rockfall. In general, the working face had an uneven contour and barely any visible hole profiles (Figure

A typical working face with overbreak and underbreak after two-step blasting.

The unsuccessful blasting in Banjie tunnelling is mainly caused by inappropriate charging. When continuous charging structure is used at the hole bottom, the over concentrated charging in this section is prone to bring about heavy shock pressure to the borehole wall. The uncharged hole collar, however, tends to result in an underbreak due to insufficient shock pressures.

The unsuccessful blasting is mainly attributable to improper charging. With continuous bottom charging, the charged bottom applied a heavy shock pressure onto borehole wall, while the uncharged hole collar generated so few shock pressure as to cause underbreak. In light of these, Starfield superposition was introduced considering the attenuation and superposition of blasting pressure, and the theoretical solution of the initial borehole wall pressure was obtained for top and middle air-deck blasting.

Meanwhile, the author constructed a stable dynamic pressure test system that avoids the interference and signal distortion of the previous test method and validated the theoretical analysis results through model tests. To determine the optimal axial decoupling coefficient, the distribution features of the initial borehole wall pressure were analysed under different axial decoupling coefficients and contrasted with each other by numerical simulation.

Based on the findings, the peripheral hole charging structure was optimized for the blasting of Grade III rocks in Banjie tunnel, aiming to enhance the smooth blasting effect. Then, the damping effect of air-deck blasting was compared with that of the blasting with continuous bottom charging.

Starfield superposition treats the column charge as the superposition of a finite number of spherical charges with equal radius, that is, the equal charging principle. Let_{c} and_{e} be the diameter of column charge and the equivalent radius of spherical charge, respectively. Then, the equal charging principle can be expressed as

For simplicity, it is assumed that the peak pressure pattern remains the same independent of the detonation order of spherical charges in each unit, such that the peak pressure at a point in the air gap equals the pressure of the shock wave at the point produced by the blasting of the equivalent unit spherical charge lying the closest to the air gap. This value is close to the actual peak pressure and thus satisfies the computing demand [

By Starfield superposition, the time effect of the explosion of unit spherical charge cannot be ignored while computing the blasting effect of the column charge. This is because both the detonation velocity of explosives and the longitudinal wave velocity of rock are both in the 10^{3} m/s order of magnitude. Hence, the following exponential function was adopted to depict the time attenuation of the shock wave induced by unit spherical charge [_{p}(1-2_{p}(1-2_{p} is the longitudinal wave velocity of rock;

For a point in the air gap, each equivalent unit spherical charge has a pressure effect on the time of positive pressure. Without the loss of generality, the peak pressure is assumed to occur when the shock wave induced by a unit spherical charge arrived at a specified point. For example, the pressure of a point in the air gap reaches the peak when the shock wave induced by spherical charge unit_{i} is the distance from unit spherical charge_{k} is the distance from unit spherical charge

In accordance with the shock wave theory, the peak pressure of shock wave attenuates with the distance, under a single spherical charge, following the pattern below [_{s}_{s} is the actual charge quantity;

According to (

Thus, (

For better accuracy, the attenuation coefficient of shock pressure along the borehole axis is denoted as

When ignoring the interaction of explosion for adjacent unit spherical charges, the peak pressure at the specified point of the column charge can be approximately considered as the superposition of the peak stress at the point of all spherical charges.

In the upper air-decked charging structure, the length of the air gap is assumed as_{a}, the charge length at hole bottom as_{e}, and the charge diameter is_{c}. As shown in Figure _{a}) away from the top of the charging section. At the blasting of the unit spherical charge

Initial shock pressure of borehole wall with upper air-decked charge.

In this case, the shock pressure produced by the entire section of column charges at point A equals the pressure superposition of n unit spherical charges at that point:

In the middle air-decked charging structure, the length of the air gap is assumed as_{a}, the charge length at hole bottom as_{e}, and the length of upper charging section and the lower charging section are_{1} and_{2}, respectively. As shown in Figure _{a}) away from the top of the lower charging section. At the blasting of the unit spherical charge

Initial shock pressure of borehole wall with middle air-decked charge.

At the blasting of the unit spherical charge

In this case, the shock pressure produced by the upper and lower charging sections at point A’ equals the pressure superposition of all unit spherical charges at that point:_{1 }and_{2} are the number of equivalent unit spherical charges in the upper and lower charging sections, respectively.

The variation curve of the initial shock pressure along the borehole axis of the upper and middle charging structures were derived by (

Variation in initial shock pressure of borehole wall.

Based on the principle of resistance strain, the pressure test system applies a dynamic pressure on the specimen, and the resulting deformation of the specimen is recorded by the strain gauges at the measuring points. Then, the deformation-induced resistance change is converted into the change of voltage or current, making it possible to deduce the value of deformation. Here, the pressure at each monitoring point is approximated by Hooke’s law, with the aim of reflecting the distribution features of the initial shock pressure of borehole wall along the axial direction.

The test instruments include a Blast-Ultra multichannel shock tester (Chengdu Tytest Co., Ltd.), a KD6009A strain amplifier (Yangzhou Kedong Electronics Co., Ltd.), etc. The strain gauges are attached to prefabricated strain bricks and embedded in a concrete model to receive the explosive signals. The entire test system is illustrated in Figure

Pressure test system.

The 40cm×20cm×50cm (L×W×H) cement mortar model was casted with 42.5# ordinary portland cement and screened fine sands (size: <1mm) at the mix proportion of 1:1:0.5 (cement: sand: water). The model was cured for 28 days at room temperature. The holes (depth: 40cm; blasting burden: 5.5cm) were reversed by a solid fiberglass pipe (OD: 12mm) at 10cm away from the front boundary and the back boundary.

For the upper air-decked charging structure, one 2# Nonel rock detonator was installed at the hole bottom, a 28cm air gap was reserved at the upper part, and the axial decoupling coefficient_{l} was set to 5. For the middle air-decked charging structure, one 2# Nonel rock detonator was installed at the hole bottom and the hole collar, respectively, a 21cm air gap was reserved at the middle part, and the axial decoupling coefficient_{l} was set to 2.5. In both charging structures, the hole collars were blocked with 5cm long cement plugs (Figure

The cement mortar model and layout of measuring points.

Up-air-deck charge

Middle-air-deck charge

The strain bricks are 3cm×3cm×40cm (L×W×H) cuboids. These were prepared with the same mix proportion, seeking to prevent the reflection of instantaneous explosion signals and maintain a uniform wave impedance between the model and the bricks [

Before pasting the strain gauges, the specimen surface was polished with sandpaper at 45° to the axis of the strain brick to remove the sands and gravels. The strain gauges were them pasted with strong glue. The redundant glue must be squeezed out to ensure the good contact between the gauge and the stick.

In the meantime, three standard 5cm×5cm×10cm (L×W×H) specimens were produced and cured for 28 days in the same environment as the models. The physical-mechanical parameters of the models were determined after the curing (Table

Physical-mechanical parameters of the models.

Specimen number | Density (kg/m^{3}) | Longitudinal wave velocity (m/s) | Modulus of elasticity (GPa) | Compressive strength(MPa) |
---|---|---|---|---|

1 | 2247.12 | 3115 | 26.44 | 20 |

2 | 2153.24 | 3067 | 25.85 | 30 |

3 | 2177.00 | 3139 | 24.50 | 20 |

Average | 2192.45 | 3100 | 25.50 | 23.33 |

The experimental parameters are as follows: sampling rate=4 each/min, data collection time=10ms, negative delay=1ms, trigger level=5%, gain=100, bridge voltage=2V, and the low-pass frequency=1kHz. The shock pressures of upper and middle air-decked charging structures are recorded in Table

Experimental results of upper and middle air-decked charging structure.

Charge structure | Measuring point | Distance from hole bottom (m) | Relative distance from hole bottom | Peak voltage (V) | Peak strain | Peak pressure (MPa) |
---|---|---|---|---|---|---|

Up-air-deck charge structure | 1 | 0 | 0 | 2.895 | 14092 | 359.346 |

2 | 0.035 | 2.92 | 3.106 | 15118 | 385.505 | |

3 | 0.070 | 5.83 | 2.836 | 14180 | 361.590 | |

4 | 0.105 | 8.75 | 2.106 | 10530 | 268.515 | |

5 | 0.175 | 14.58 | 1.042 | 5210 | 132.855 | |

6 | 0.245 | 20.41 | 0.332 | 1660 | 42.330 | |

7 | 0.315 | 26.25 | 0.195 | 975 | 24.863 | |

8 | 0.385 | 32.08 | 0.162 | 810 | 20.655 | |

| ||||||

Middle-air-deck charge structure | 1 | 0 | 0 | 3.345 | 16725 | 426.488 |

2 | 0.035 | 2.92 | 3.504 | 17521 | 446.778 | |

3 | 0.070 | 5.83 | 3.258 | 16290 | 415.395 | |

4 | 0.105 | 8.75 | 2.421 | 12105 | 308.678 | |

5 | 0.140 | 11.67 | 1.273 | 6365 | 162.308 | |

6 | 0.175 | 14.58 | 1.188 | 5940 | 151.470 | |

7 | 0.210 | 17.50 | 1.193 | 5965 | 152.108 | |

8 | 0.245 | 20.42 | 2.285 | 11425 | 291.338 | |

9 | 0.280 | 23.33 | 3.150 | 15748 | 401.573 | |

10 | 0.315 | 26.25 | 3.512 | 17559 | 447.753 | |

11 | 0.350 | 29.17 | 3.276 | 16377 | 417.608 |

Figures

For the upper air-decked charging structure, the initial shock pressure of the charging section followed a convex distribution, with the peak value near the charge centre. With the increase in the distance from the charging section, the borehole wall shock pressure in the air gap underwent a sharp decline initially before reaching a relatively constant level. The minimum pressure was observed at the hole collar.

For the middle air-decked charging structure, the pressures at both ends of the charging section obeyed a convex distribution, with the peak value near the charge centre. By contrast, the pressure in the air gap was exhibited as a concave distribution and minimized at the middle of the air column.

In both the upper and middle air-decked charging structures, the initial borehole wall shock pressure increased with the decrease in the distance from the charging section. When that distance was on the rise, the initial pressure experienced a gradual decrease. The decline rate was fast at the beginning and slow on the later stage. In the end, the borehole wall shock pressure reached a relative stable state.

In the middle air-decked charging structure, the pressure values at major monitoring points in the air gap were close to the minimum value. This feature was particularly prominent when the air space was fairly long. Besides, the initial shock pressure in the upper and lower charge sections obeyed the same distribution of that in the upper air-decked charging structure. The initial shock pressure distribution of the two charge sections could be combined into the superposed impact pressure.

Variation in initial borehole wall pressure with relative distances from hole bottom (upper air-decked charging structure).

Variation in initial borehole wall pressure with relative distances from hole bottom (middle air-decked charging structure).

To sum up, the axial distribution curve of the initial borehole wall shock pressure in the two charging structures agrees well with that of the theoretical analysis.

Five numerical models were established to verify the accuracy of the theoretical formula derived by Starfield superposition, which calculates the blast-induced initial shock pressure in the air gap. The numerical simulation considers both upper and middle air-decked charging structures, as well as five different charging lengths. In these models, the column charge was 1~4 times longer than equivalent spherical charge. For the middle air-decked charging structure, the lengths of the upper and lower charging sections are both 1~5 times of the diameter of equivalent spherical charge.

As shown in Figure

Numerical simulation models.

For better accuracy, the rock, explosive, and air were described separately by

Material model and state equation parameters of the rock.

Density (kg/m^{3}) | Modulus of elasticity (GPa) | Poisson ratio | Yield stress (MPa) | Tangent modulus (GPa) | Hardening coefficient |
---|---|---|---|---|---|

2350 | 61.0 | 0.31 | 75.0 | 2.0 | 1.0 |

Material model and state equation parameters of the explosive.

Density (kg/m^{3}) | Explosion velocity (m/s) | Detonation pressure (GPa) | | | _{ 1 } | _{ 2 } | | _{ 0 } (GPa) | |
---|---|---|---|---|---|---|---|---|---|

1300 | 4000 | 5.2 | 211.4 | 0.182 | 4.2 | 0.9 | 0.15 | 4.192E6 | 1.0 |

Note: _{1}, _{2}, and _{1} and _{2} are nondimensional parameters; _{0} is initial internal energy per unit volume of explosive;

Material model and state equation parameters of the air.

Density (kg/m^{3}) | _{ 0 } | _{ 1 } | _{ 2 } | _{ 3 } | _{ 4 } | _{ 5 } | _{ 6 } | _{ 0 } (GPa) | |
---|---|---|---|---|---|---|---|---|---|

1.29×10^{−2} | 0 | 0 | 0 | 0 | 0.4 | 0.4 | 0 | 0 | 1.0 |

Note: _{0} ~ _{6} are multinomial coefficients of the state equation; _{0} is initial internal energy per unit volume of explosive;

The intersection points between the borehole wall and the axial cross-section of air column, which is far away from free faces, were selected to monitor the initial shock pressure of borehole wall. Through simulation, two sets of initial shock pressure values were obtained from the monitoring points for upper and middle air-decked charging structures. Meanwhile, the shock pressures at the specified points were acquired through theoretical analysis.

Figure

The variation in initial shock pressure with column lengths at specified points.

Furthermore, the theoretical and simulated initial shock pressure at specified points of the air gap increased with the charging length, according to the variation in initial shock pressure with column lengths at specified points. The trend echoes with the classical blasting theory.

The author established the numerical models by ANSYS/LS-DYNA, using the same dimension, borehole size, and borehole pattern with the test model (Figure _{l}=2.5,_{l} =3.5,_{l} =4,_{l}=5.0, and_{l} =6.0. Among them,_{l} =5.0 corresponds to the charging structure of the test model. In this charging structure, the overall charging length equals the length of the lower charging section.

Numerical simulation models.

For the middle air-decked charging structure, five models were created with different axial decoupling coefficients:_{l}=2.5,_{l} =3.5,_{l} =4,_{l}=5.0, and_{l} =6.0. Among them,_{l} =2.5 corresponds to the charging structure of the test model. The charging parameters of these models are shown in Table

The charging parameters.

Axial decoupling coefficients | Hole length (cm) | Stemming length (cm) | Air column length (cm) | Charge length (cm) | ||
---|---|---|---|---|---|---|

Total length (cm) | Upper length (cm) | Lower length (cm) | ||||

2.5 | 40 | 5 | 21 | 14 | 4.7 | 9.3 |

3.5 | 40 | 5 | 25 | 10 | 3.3 | 6.7 |

4.0 | 40 | 5 | 26.25 | 8.75 | 2.9 | 5.85 |

5.0 | 40 | 5 | 28 | 7 | 2.3 | 4.7 |

6.0 | 40 | 5 | 29.16 | 5.84 | 1.95 | 3.89 |

The material models of the rock, explosive, and air and the relevant state equations (Tables

Parameters of the stemming material.

Density (kg/m^{3}) | Shear modulus (GPa) | Bulk modulus(GPa) | _{ 0 } | _{ 1 } | _{ 2 } | | | |
---|---|---|---|---|---|---|---|---|

1800 | 1.60E-2 | 1.328 | 0.0033 | 1.31E-7 | 0.1232 | 0.0 | 0.0 | 0.05 |

| ||||||||

| | | | | | | | _{ 1 }(GPa) |

| ||||||||

0.09 | 0.11 | 0.15 | 0.19 | 0.21 | 0.221 | 0.25 | 0.30 | 0.0 |

| ||||||||

_{ 2 } (GPa) | _{ 3 } (GPa) | _{ 4 } (GPa) | _{ 5 } (GPa) | _{ 6 } (GPa) | _{ 7 } (GPa) | _{ 8 } (GPa) | _{ 9 } (GPa) | _{ 10 } (GPa) |

| ||||||||

3.42 | 4.53 | 6.76 | 12.70 | 20.80 | 27.10 | 39.20 | 56.60 | 123.0 |

Note: _{0}, _{1}, and _{2} are constants of yield function; _{1} ~ _{10} are pressures corresponding to characteristic bulk strains.

To capture the initial borehole wall shock pressure, row elements were selected from borehole wall as pressure monitoring points along the axial direction from hole bottom to hole collar. Figures

Initial shock pressure of borehole wall with upper air-decked charging structure.

Initial shock pressure of borehole wall with middle air-decked charging structure.

As shown in Figures _{l }= 5.0 of the upper air-decked charging structure and_{l }=2.5 of the middle air-decked charging are consistent with the theoretical results and the experimental findings. Suffice it to say that the simulation demonstrates the reliability of theoretical analysis and physical experiments.

The borehole length in a single blasting row is relatively long in Grade III surrounding rock of Banjie tunnel. To ensure the effect of smooth blasting, the peripheral hole was designed with air-decked charging structure. In the middle air-decked charging structure, the initial borehole wall shock pressure obeyed a wavy distribution (peak value> valley value>0). The peak and valley values, respectively, correspond to the charging section and the air gap. To achieve a consistent impedance of the explosive and rock, it is necessary to appropriate the length of the air column [

In Banjie tunnel, the compressive strength and tensile strength of Grade III surrounding rock are 75MPa and 5.6MPa, respectively (Table _{l }=2.5~6. This means blasting cracks formed among the adjacent peripheral holes. However, the shock pressures at major monitoring points in the air gap were above the compressive strength of the rock, when_{l}=2.5, _{l} =4.0, and_{l} =5.0. The result shows that the rock was crushed but not sufficient to achieve a good smooth blasting effect.

In contrast, when_{l} =6.0, the pressures at most monitoring points in the air gap were close to the valley value, except the charging section and a small portion of the air gap, and were below the compressive strength of the rock. In this case, the surrounding rock remained integrated after the blast and kept a half-hole profile, revealing enhanced smooth blasting effect. Therefore, the axial decoupling coefficients of the peripheral hole were designed as_{l} =6.0 in Grade III surrounding rock of Banjie tunnel. In light of the field conditions, four-stage charges and three air-gaps were adopted for tunnelling. The optimized charging structure of peripheral hole in Grade III rock is given in Figure

Optimized charging structure of peripheral hole in Grade III surrounding rock.

In Figure

Optimized smooth blasting effect of Grade III surrounding rock.

In tunnel blasting, the vibration, a key impact factor of rock stability, is the combined effect of the blasting of cutting holes, auxiliary holes, and peripheral holes. However, it is difficult to accurately extract the variation induced by the blasting of peripheral holes in field monitoring. To compare the blasting vibration of continuous bottom charging with air-decked charging structure, two 100cm×20cm×60cm (L×W×H) cement mortar models, denoted as model I and model II, respectively, were prepared for blasting experiment.

The mix proportion, curing environment, and curing time were exactly the same as the cement mortar models of Section

The cement mortar models and layout of vibration measuring points.

The monitoring results are shown in Table

Comparison of blasting vibration vector synthesis velocity.

Distance from explosive source(cm) | 10 | 20 | 40 | 80 |
---|---|---|---|---|

Vector synthesis velocity of blasting vibration in model I(cm/s) | 20.1759 | 9.3194 | 6.0529 | 3.4562 |

| ||||

Vector synthesis velocity of blasting vibration in model II(cm/s) | 17.3309 | 8.0813 | 5.1540 | 2.9053 |

| ||||

Relative decreasing amplitude ratio (%) | 14.10 | 15.32 | 14.85 | 15.94 |

Typical waveforms of blasting vibration vector synthesis velocity.

Based on Starfield superposition, the theoretical solutions of the initial pressure on borehole wall were obtained for upper and middle decked charged structures. Through field monitoring and numerical simulation, it is learned that the initial borehole wall pressure was unevenly distributed at long air columns.

For the upper air-decked charging structure, the initial shock pressure of the charging section followed a convex distribution, with the peak value near the charge centre. With the increase in the distance from the charging section, the borehole wall shock pressure in the air gap underwent a sharp decline initially before reaching a relatively constant level. The minimum pressure was observed at the hole collar. For the middle air-decked charging structure, the pressures at both ends of the charging section obeyed a convex distribution, with the peak value near the charge centre.

The deviations between simulated and theoretical pressures are smaller than 10%, indicating the reliability of the theoretical formula derived by Starfield superposition. It is concluded that this formula works well in computing the blasting-induced initial shock pressure in the air gap under both upper and middle air-decked charging conditions.

Compared with the continuous bottom charging, the air-decked charging is suitable to the actual conditions thanks to the distribution features of initial borehole wall shock pressure. The application of the structure in Grade III surrounding rock of Banjie tunnel led to an expected smooth blasting effect.

The research findings provide valuable references to the theoretical and experimental calculation of air column length and other key parameters of air-deck blasting and shed new light on the charging structure determination of smooth blasting and blasting vibration control for the excavation of large-section, deep mining roadways.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research work was supported by the National Natural Science Foundation of China under Grants 51679093 and 51374112.