Energy Distribution of Shock Wave in Deep Rock Mass Blasting

doi:10.12382/bgxb.2023.0254

Abstract

Abstract:

In-situ stress has a significant effect on the distributions of the rock mass stress induced by explosion and the explosion energy. To elucidate the distribution characteristics of explosion energy in deep rock mass, the distribution of rock mass stress under the action of in-situ stress and explosion load is calculated using the superposition principle. Subsequently, the failure characteristics of deep rock mass under shock waves are determined using the rock mass failure criterion. The proportions of shock wave energy that causes blasting cavity expansion, radial crack propagation, and rock mass elastic deformation under different conditions are analyzed. Furthermore, a numerical simulation method is employed to investigate the impact of in-situ stress on the distribution of shock wave energy in the rock mass. The results demonstrate that the characteristics of rock mass, the performance of explosive, and the levels of in-situ stress significantly affect the energy distribution. The proportion of total energy of shock waves transmitted into hard rock (granite) and the proportion of effective energy are smaller than those in soft rock (shale) under high in-situ stress environment. Compared with low-performance explosives, when using high-performance explosives for blasting, the proportion of total energy of shock waves transmitted into granite and the proportion of effective energy are greater. With the increase of in-situ stress, the proportion of shock wave energy for the blasting cavity expansion is basically unchanged, the proportion of shock wave energy for radial crack propagation decreases linearly, and the proportion of shock wave energy for rock mass elastic deformation increases exponentially. The effective energy is relatively small although the proportion of the total energy of shock waves is larger under the higher in-situ stress. The findings can provide a reference for improving the energy distribution of shock wave in deep rock mass blasting and enhancing the blasting effect of rock mass.

Key words: deep rock mass, blasting, shock wave energy, high in-situ stress, energy distribution

CLC Number:

O389

YANG Jianhua, PENG Chao, YE Zhiwei, LENG Zhendong, WEI Bin. Energy Distribution of Shock Wave in Deep Rock Mass Blasting[J]. Acta Armamentarii, 2024, 45(6): 1735-1746.

Figures/Tables 17

Fig.1 Schematic diagram of combined action model of explosion load and in-situ stress

Table 1 Calculation of shock wave failure range

工况编号	岩体类型	炸药类型	地应力水平
工况编号	岩体类型	炸药类型	σ_v/MPa	σ_h/MPa
EI-1	页岩、石灰岩、花岗岩	硝铵炸药	50	50
EI-2	花岗岩	乳化炸药、硝铵炸药、铵油炸药	50	50
EI-3	花岗岩	硝铵炸药	0、10、20、30、40、50、60	0、10、20、30、40、50、60

Table 2 Mechanical parameters of rock mass

岩体类型	ρ_m/ (kg·m^-3)	C_p/ (m·s^-1)	σ_c/ MPa	σ_t/ MPa	E_m/ GPa	μ₀
页岩	2000	1950	50	5.6	18.0	0.28
石灰岩	2600	3430	110	10.0	32.5	0.24
花岗岩	2670	5500	180	15.0	70.0	0.22

Table 3 Explosive parameters in theoretical calculation

炸药类型	ρ₀/(kg·m^-3)	D/(m·s^-1)	Q/(MJ·kg^-1)
乳化炸药	1300	4000	4.19
硝铵炸药	1000	3600	3.76
铵油炸药	1100	2700	2.80

Fig.2 Damage zone range induced by shock waves under different conditions

Fig.3 Energy distribution of shock wave under different rock conditions (AN-TNT, σv=σh=50MPa)

Fig.4 Energy distribution of shock wave under different explosive conditions (granite,σv=σh=50MPa)

Fig.5 Energy distribution of shock waves under different in-situ stresses

Fig.6 Schematic diagram of model

Table 4 RHT model parameters of rock

参数	数值
密度ρ_r/(kg·m^-3)	2660
剪切模量G/GPa	21.9
剪压强度比 $f s *$	0.18
拉压强度比 $f t *$	0.04
EOS多项式参数T₁/GPa	35.27
EOS多项式参数T₂/GPa	0
初始损伤参数D₁	0.04
损伤参数D₂	1.0
雨贡纽系数A₁/GPa	35.24
雨贡纽系数A₂/GPa	39.58
雨贡纽系数A₃/GPa	9.04
失效面参数A_f	1.60
失效面指数n	0.61
残余应力强度参数A_f	1.60
残余应力强度指数n_f	0.61
EOS多项式参数B₀	1.22
EOS多项式参数B₁	1.22
参考压缩应变率EOC	3×10^-5
参考拉伸应变率EOT	3×10^-5
失效压缩应变率EC	3×10²⁵
失效拉伸应变率ET	3×10²⁵
拉压子午比参数Q₀	0.68
罗德角相关系数B_l	0.01
压缩屈服面参数GC*	0.53
拉伸屈服面参数GT*	0.7
孔隙压缩时压力P_el/MPa	125
孔隙压实时压力P_comp/GPa	6
剪切模量缩减系数ξ	0.5
侵蚀塑性应变EPSF	2.0
最小失效应变 $ε p m$	0.01
孔隙度指数N	3.0
初始孔隙度a₀	1.0
压力对拉伸下塑性流动的影响PTF	0.001
拉伸应变率指数β_t	0.036
单轴抗压强度f_c/MPa	167.8
压缩应变率指数β_c	0.032
格林艾森常数GAMMA	0

Table 4 RHT model parameters of rock

参数	数值
密度ρ_r/(kg·m^-3)	2660
剪切模量G/GPa	21.9
剪压强度比 $f s *$	0.18
拉压强度比 $f t *$	0.04
EOS多项式参数T₁/GPa	35.27
EOS多项式参数T₂/GPa	0
初始损伤参数D₁	0.04
损伤参数D₂	1.0
雨贡纽系数A₁/GPa	35.24
雨贡纽系数A₂/GPa	39.58
雨贡纽系数A₃/GPa	9.04
失效面参数A_f	1.60
失效面指数n	0.61
残余应力强度参数A_f	1.60
残余应力强度指数n_f	0.61
EOS多项式参数B₀	1.22
EOS多项式参数B₁	1.22
参考压缩应变率EOC	3×10^-5
参考拉伸应变率EOT	3×10^-5
失效压缩应变率EC	3×10²⁵
失效拉伸应变率ET	3×10²⁵
拉压子午比参数Q₀	0.68
罗德角相关系数B_l	0.01
压缩屈服面参数GC*	0.53
拉伸屈服面参数GT*	0.7
孔隙压缩时压力P_el/MPa	125
孔隙压实时压力P_comp/GPa	6
剪切模量缩减系数ξ	0.5
侵蚀塑性应变EPSF	2.0
最小失效应变 $ε p m$	0.01
孔隙度指数N	3.0
初始孔隙度a₀	1.0
压力对拉伸下塑性流动的影响PTF	0.001
拉伸应变率指数β_t	0.036
单轴抗压强度f_c/MPa	167.8
压缩应变率指数β_c	0.032
格林艾森常数GAMMA	0

Table 5 Explosive parameters for numerical calculation

ρ₀/ (kg·m^-3)	D/ (m·s^-1)	A/ GPa	B/ GPa	R₁	R₂	ω	p_cj/ GPa	E₀/ GPa
1320	6690	586	21.6	5.81	1.77	0.282	16	7.38

Fig.7 Comparison of simulated and laboratory test crack distributions

Fig.8 Failure characteristics of rock mass around the hole

Fig.9 Flowchart of area calculation

Fig.10 Damage characteristics of rock mass under different in-situ stresses

Fig.11 Stress-time curve of Point P

Fig.12 Proportion of elastic vibration energy under differentin-situ stresses in numerical simulation

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