Numerical Analysis of Impact of Shot Hole Spacing on Crack Growth in Rock
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摘要: 为实现对岩石的充分破碎，有效利用炸药能量，基于有限元分析软件ANSYS/LS-DYNA及流固耦合（ALE）算法，研究了不同炮孔间距对岩石（角岩）爆炸裂纹扩展的影响，同时将模拟结果应用在工程实践上加以验证。结果表明：随着两炮孔间距离的增大，单炮孔周围裂纹扩展更加充分，炮孔周围粉碎区增大，萌生的分支小裂纹逐渐减少，主裂纹增多。在两炮孔之间受到相邻炮孔爆炸应力波影响的区域，主裂纹发育扩展较为明显，且随着炮孔间距的增大，主裂纹相互贯通的位置越靠近两炮孔中心连线方向。工程实践表明：数值模拟结果与爆破工程效果具有较好的吻合性，将数值模拟结果用来指导爆破方案设计是可行的，能够为爆破工程提供重要的参考。Abstract: In order to achieve full fragmentation of the rock and effectively use the explosive energy, the impact of different hole spacing on the rock (hornfels) blast crack extension was studied via ANSYS/LS-DYNA software package using fluid-structure interaction (ALE) algorithm. The results showed that with the increase of the distance between the two holes, the crack growth around the single gun hole becomes more sufficient, the comminution area around the gun hole increases, the generated branch small crack gradually decreases, the main crack increases, and the crack growth rate is about 0.42 times that of the longitudinal wave velocity of the rock. In the area between the two holes affected by the explosion stress wave of the adjacent holes, the main crack growth and expansion are more obvious, and with the increase of hole spacing, the position of the main crack interconnection is closer to the direction of connecting the center of the two holes. Engineering practice suggested that the results of numerical simulation has positive effect on blasting engineering, the results of numerical simulation can be used to guide the design of blasting scheme and can provide important reference value for the blasting engineering.
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Key words:
- finite element /
- fluid-solid coupling /
- crack propagation /
- blasthole spacing /
- spallation
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图 5 不同孔间距下炮孔中心连线中点处x方向的压力曲线
Figure 5. Pressure curve in the x direction at the center of the connecting line of gun hole with different hole spacing
${\rho}$/(kg·m–3) E0/GPa ${\mu}$ ${{\sigma _0}}$/MPa Etan/GPa ${{\sigma _{\rm{c}}}}$/MPa ${{\sigma _{{\rm{st}}}}}$/MPa C/s–1 P 2700 68.69 0.228 75 40 150 5.6 2.63 3.96 
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${\rho}$/(kg·m–3) D/(m·s–1) pCJ/GPa A/GPa B/GPa R1 R2 ${\omega}$ 1200 4000 4.80 214 0.093 4.15 0.95 0.3
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表 3 岩石裂隙扩展平均速度
Table 3. The average speed of rock crack extension
Speed of rock crack extension/（m·s−1） V/Cp L=40 cm L=60 cm L=80 cm 2051（t=40 ${{\text{μ}}{\rm{s}}}$） 2157（t=60 ${{\text{μ}}{\rm{s}}}$） 2286（t=70 ${{\text{μ}}{\rm{s}}}$） 0.39 2197（t=70 ${{\text{μ}}{\rm{s}}}$） 2083（t=120 ${{\text{μ}}{\rm{s}}}$） 2285（t=140 ${{\text{μ}}{\rm{s}}}$） 0.41 1656（t=230 ${{\text{μ}}{\rm{s}}}$） 1923（t=210 ${{\text{μ}}{\rm{s}}}$） 2140（t=190 ${{\text{μ}}{\rm{s}}}$） 0.44 1968（Average） 2054（Average） 2237（Average） 0.41
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表 4 爆破参数表
Table 4. Blasting parameters
H/m h/m a/m b/m L/m l/m Q/kg 1.7 0 2.0 1.2 0.20 1.50 0.9 2.0 0 2.0 1.2 0.22 1.78 1.0 2.5 0 2.5 1.5 0.45 2.05 2.0 3.0 0 3.0 1.5 0.67 2.33 3.0
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表 5 振动监测表
Table 5. Blasting vibration monitoring
Measuring point Distance/m vx/(cm·s–1) fx/Hz vy/(cm·s–1) fy/Hz vz/(cm·s–1) fz/Hz 1 163 –0.21 9.16 –0.28 9.16 0.27 18.31 2 154 0.04 8.85 0.04 35.71 0.03 9.48 3 339 0.04 12.16 0.05 7.83 0.06 13.29 4 234 0.19 18.31 –0.14 9.16 –0.11 18.31
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