3.2.1. Shallow-Hole Blasting Range Law
The immediate roof is strongly influenced by the blasting-induced dynamic impacts. The roof rock can be classified into a crushing zone (I), crack zone (II), and elastic deformation zone (III), based on the degree of damage of the rock due to the blasting.
Figure 5 schematically shows the classification of roof rock caused by the shallow-hole blasting. A detailed discussion on the classification of roof rock is also presented below [
19,
20,
21,
22].
(I) Crushing zone
The explosive energy is partially consumed by the compression or crushing of the rock, forming a crushing zone near the borehole (I zone in
Figure 5). Under uncoupled charge conditions, the radius of the crushing zone can be calculated as follows:
where
is the explosive density (kg/m
3),
is the explosive detonation velocity (m/s),
is the rock uniaxial compressive strength (MPa),
is the radius of the blast hole (m),
, and
and
are the the rock density (kg/m
3) and the longitudinal wave velocity (m/s).
(II) Rupture zone
As the propagation range of stress waves increases, the energy density per unit area of rock decreases. The stress wave is propagated away from the crushing zone. If the maximum tensile stress is larger than the dynamic tensile strength of the rock, cracks would accordingly occur and the rupture (crack) zone is formed (II zone in
Figure 5). The radius of the crack zone can be calculated as follows:
where
ν is the Poisson’s ratio of the rock, and
is the rock uniaxial tensile strength (MPa).
(III) Elastic deformation zone
The stress waves are further decreased when propagating further away from the borehole. The decreased dynamic stress cannot cause fracture of the rock and can only induce elastic deformation (III zone in
Figure 5). The radius of the elastic deformation zone can be calculated by
where
Q is the quality of explosives for a single hole (kg).
According to the used explosives and blast-hole parameters, the geology conditions in the 72207 working face in the Sanhejian colliery were determined as = 1200 kg/m3, = 3600 m/s, = 65.43 MPa, = 2.1 × 10−2 m, = 2.7 × 103 kg/m3, Cp = 3000 m/s, ν = 0.22, = 5.8 MPa, and Q = 2.4 kg. The above parameters were substituted into Equations (1)–(3), and the radius of the crushing zone was calculated to be 0.29 m, the radius of the crack zone was found to be 0.34 m, and the radius of the elastic zone was determined to be 2.0–2.68 m.
3.2.2. Determination of Critical Parameters for Shallow Blasting
(1) Blasting depth of shallow-hole blasting
The depth of the blasting hole influences the effects of blasting on weakening the roof strata and eventual roof strata caving [
23]. The blasting hole depth was determined by Equation (4) according to the geological conditions of the 72207 working face in the Sanhejian colliery. The average thickness of the immediate roof of the 72207 working face is 1.0 m. The average thicknesses of the main roof and coal seam are 6.8 m and 2.4 m.
where
H is the hole depth (m),
M is the mining height (m), and
is the rock’s expansion coefficient.
The mining height M = 2.4 m and the rock’s expansion coefficient = 1.5 were substituted into Equation (4), giving H = 4.8 m. Based on the theoretical analysis and the author’s field experience, the design hole depth was selected as 5.0 m in order to achieve the designed blasting effects. The inclination angle to the gob side of 10° was selected to facilitate the drilling process and the subsequent roof strata caving.
(2) Explosive parameters of shallow-hole Blasting
According to the China Coal Mine Safety Regulations [
24], the second-grade permissible explosive for the mining industry was selected for the shallow-hole blasting in the 72207 face, as Sanhejian colliery is characterized as a low-gas mine. The explosive density and the detonation wave propagation velocity have direct impacts on the blasting effect. The second-grade permissible explosive cartridge has a length of 300 mm, a diameter of 27 mm, and a weight of 0.3 kg per block, with a detonation rate of 3600 m/s and a density of 1200 kg/m
3. Each cumulative energy tube is 1.4 m long and can contain four explosive cartridges. A detonator is installed in the last explosive cartridge for each cumulative energy tube.
To facilitate the installation of the explosives, the inner diameter of the cumulative energy tube is required to be larger than the diameter of the explosive cartridge, and the outer diameter of the cumulative energy tube should be smaller than the diameter of the borehole. Boreholes of 42 mm in diameter were drilled in the roof strata. The diameter of the explosive cartridge was 27 mm. Hence, the cumulative energy tubes with an outer diameter of 32 mm and an inner diameter of 29 mm were used.
(3) The spacing between the shallow blasting boreholes
Numerical analysis using the nonlinear dynamic analysis software LS-DYNA was carried out to analyze the influences of the borehole spacing on the blasting effects. The ALE (Arbitrary-Lagrangian-Eulerian) method and multi-material fluid–solid coupling method were adopted when establishing the numerical model [
25]. The measuring points were set in the middle point of the two holes to monitor the variation of the effective stress within the rock. The model size was 6000 mm × 5000 mm × 5000 mm, the hole diameter was 42 mm, the diameter of the explosive cartridge was 27 mm, and the depth of the hole was 5000 mm, as shown in
Figure 6.
The JWL (Jones-Wilkens-Lee) equation was adopted in LS-DYNA3D to describe the relationship between the pressure applied to the borehole wall by a unit detonation product and the volume of the detonation product (Equation (5)).
where
P is the explosive detonation unit pressure (MPa),
E0 is the explosive detonation product initial density,
V is the explosion detonation product relative volume, and
A, B, R1, R2, and
are explosive material constants determined from the experiment, as shown in
Table 3.
Explosive parameters and JWL equation parameters are given in
Table 3. The rock material model adopts the kinematics hardening plastic model. The rock mechanical parameters used in the numerical analysis are shown in
Table 4.
The effects of the borehole spacing
The effective stress curve at the monitoring points was obtained for different hole spacings of 0.8 m, 1.0 m, and 1.2 m using the post-processing module LS-PREPOST (Livemore software of pre and post-processor in LS-DYNA, as shown in
Figure 7.
The following can be seen from
Figure 7:
(1) The increase in hole spacing decreased the effective stress. A smaller hole spacing led to a greater effective stress peak at the monitoring point. The peak effective stresses for the hole spacings of 0.8, 1.0, and 1.2 m were 78.3, 49.5, and 44.7 MPa, respectively.
(2) The effective stress reduced with time and tended to become stable around a certain value, which decreased with the increase in hole spacing. The stable effective stresses for the hole spacings of 0.8, 1.0, and 1.2 m were 45, 20, and 10–20 MPa, respectively.
(3) The rock breaks when the stable effective stress is greater than the dynamic tensile stress of the rock. The stable effective stresses generated when the hole spacings were 0.8 and 1.0 m were greater than the dynamic tensile strength of the rock. When the hole spacing was 1.2 m, the effective stress was less than the dynamic tensile strength of the rock. Thus, the spacing of the blasting holes was determined as 1.0 m.
The evolution of the effective stress in shallow-hole blasting
The evolution of the effective stress in the rock at the hole spacing of 1.0 m is shown in
Figure 8.
It can be seen from
Figure 8 that, when the blasting time was 39.886 μs (
Figure 8a), the range of the explosive stress wave reached 138 mm. The stress wave propagated in the rock mass with time, and the stress waves of the adjacent holes met and overlapped in the middle point at 139.84 μs. The stress superposition at the middle point increased with time, and the effective stress reached the maximum value of 49.5 MPa at 299.51 μs, which exceeds the dynamic tensile strength of 18 MPa. The stress superposition effect decreased, and the effective stress reduced to 20 MPa, which is still larger than the dynamic tensile strength of the roof strata.