Damage and Fractal Analysis of Double-Hole Blasting
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摘要: 采用理论分析和模型试验研究双孔爆破介质的损伤破坏特征，基于双孔爆破模型的弹性力学平面应变问题解析，建立了双孔爆破动态应力场演化的理论模型。通过模型试验研究了不同炮孔间距下双孔爆破的损伤特征，通过分区和分形维数定量表征了炮孔周围不同区域的损伤特征。结果表明：随着炮孔间距的增大，应力波叠加作用降低，压碎区半径增大，裂纹数先减少后增多，主裂纹的平均长度逐渐增大；炮孔连线方向的损伤逐渐减小，垂直于炮孔连线方向的损伤逐渐增大；小孔距有利于裂纹孔间贯穿和沿炮孔连线方向扩展；试件左部和右部区域的损伤变量逐渐增大，中部区域的损伤变量在炮孔间距为50 mm时出现最小值；区域Ⅰ和区域Ⅱ的损伤变量先减小后增大，区域Ⅲ的损伤变量逐渐减小；在极坐标系下，区域Ⅰ的损伤均匀分布，区域Ⅱ的损伤由椭圆形分布逐渐向圆形分布转变。根据损伤区域分形维数与损伤变量的关系，构建了聚甲基丙烯酸甲酯材料双孔爆破分形损伤模型。Abstract: To investigate the damage and failure characteristics of the double-hole blasting medium, theoretical analysis and model experiments are conducted in this study. Based on the analytical solution of the elastic plane strain problem in the double-hole blasting model, a theoretical model is established to study the evolution of the dynamic stress field during double-hole blasting. The damage of double-hole blasting with different blast hole spacing is studied by the model experiment; the damage in different regions around the blast holes is analyzed by partitioned research and fractal dimension quantification. The study shows that as the blast hole spacing increases, the super position effect of stress waves decreases, the radius of the crushing zone and the average length of the main crack gradually increase, the number of cracks decreases first and then increases. Additioanlly, the increase of blast hole spacing lead to gradual decrease of the damage along the direction of the blast hole connection, while the damage perpendicular to the direction of the blast hole connection gradually increases. Small hole spacing is conducive to the penetration of cracks between holes and promotes cracks expansion along the direction of the blast hole connection. With increasing blast hole spacing, the damage variable in the left and right regions of the specimen gradually increases, and reaches a minimum value in the central region when the blast hole spacing is 50 mm. The damage variables in area Ⅰ and area Ⅱ first decrease and then increase, while the damage variable in area Ⅲ gradually decreases. The damage variable distribution in the polar coordinate system shows that area Ⅰ exhibits a uniform damage pattern, and area Ⅱ gradually transitions from an elliptical to a circular distribution. Based on the relationship between the fractal dimension of the damage area and the damage variable, a fractal damage model for double-hole blasting of poly(methyl methacrylate) (PMMA) material is constructed.
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图 6 试件压碎区半径及裂纹平均长度
Figure 6. Radius of the crushing zone of the specimen and the average length of the crack
图 8 试件不同区域的分形维数拟合曲线
Figure 8. Fractal dimension fitting curves for different regions of each specimen
图 9 各试件炮孔连线方向的分区损伤变量
Figure 9. Damage variables of each specimen in the direction of the gunnel line
图 11 双孔爆破区域Ⅰ和区域Ⅱ的损伤变量
Figure 11. Damage variables of area Ⅰ and area Ⅱ in double-hole blasting
图 12 双孔爆破损伤变量与分形维数的关系
Figure 12. Relationship between damage variables and fractal dimensions for two-hole blasting
表 1 试件损伤破坏结果
Table 1. Damage and failure results of specimens
Specimen No. Crack penetration type Radius of crushing zone/mm Number of cracks Average crack
length/mmLeft side Right side Left side Right side S-1 Penetrated 9.61 9.35 13 13 16.98 S-2 Penetrated 9.99 9.98 13 11 18.90 S-3 Penetrated 10.21 10.08 8 5 18.55 S-4 Not penetrated 12.72 12.12 13 12 19.32 S-5 Not penetrated 12.83 13.13 11 15 20.50 
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表 2 试件不同区域的损伤变量
Table 2. Damage variables in different areas of the specimen
Specimen No. Damage variables in different regions Left part Middle part Right part Left area Ⅰ Right area Ⅰ Left area Ⅱ Right area Ⅱ Area Ⅲ S-1 0.108 41 0.217 40 0.143 84 0.944 65 0.960 75 0.226 13 0.308 11 0.029 32 S-2 0.155 12 0.217 06 0.114 41 0.959 40 0.882 10 0.282 54 0.202 86 0.020 43 S-3 0.155 94 0.156 67 0.138 33 0.909 68 0.916 03 0.205 54 0.177 00 0.026 95 S-4 0.187 96 0.221 13 0.173 87 0.995 47 0.956 00 0.211 06 0.191 31 0.019 31 S-5 0.226 17 0.192 44 0.258 36 0.942 80 0.996 45 0.178 02 0.292 02 0.013 48
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