Optimization of detonation parameters for multi-point aggregated explosion effects in concrete
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摘要: 混凝土介质中多点同时或彼此微差爆炸可产生复杂的地冲击波叠加聚集效应，从而使特定作用区域内的地冲击波压力显著增强，大大提升爆炸的毁伤威力。为获取多点爆源不同排布方式下爆炸聚集效应及地冲击传播衰减规律，进行了混凝土中单点和七点聚集爆炸的现场和数值模拟试验，基于正交设计方法和灰色系统理论对多点起爆参数进行了优化设计，建立了比例装药间距、比例有源装药高度和比例起爆微差等因素与不同爆心距下峰值压力间的灰色关联度系数及灰色关联度，确定了起爆参数的优选组合，并开展了数值模拟试验检验。分析结果表明：影响地冲击聚集效应的主要因素为比例装药间距，其次为比例起爆微差，最次为比例有源装药高度。在本模拟试验情况下，采用优化的起爆参数时，即在比例装药间距为0.549 m/kg1/3、比例起爆微差为0.239 m/kg1/3和比例有源装药高度为0 m/kg1/3时，地冲击波聚集效应达到最佳，最大可达单点同等装药量产生的地冲击压力的4.7倍。Abstract: Simultaneous or slightly different explosions at multiple points in concrete medium can generate a complex superposition and aggregation effect of ground shock waves, significantly enhancing the pressure of ground shock waves in a specific area and greatly improving the destructive power of the explosion. To obtain the explosion aggregation effect and ground shock propagation attenuation law under the different arrangement of multi-point explosive sources, field tests were first carried out on single and seven-point aggregated explosions in concrete. Then, the reliability of the RHT material model parameters and the SPH numerical algorithm are verified based on experimental data. On this basis the orthogonal design method and gray system theory on the multi-point detonation parameters are adopted for design optimization. Gray correlation coefficients and gray correlations between scaled charge spacing, scaled active charge height, scaled detonation time difference and peak pressure at different proportional bursting center distances are established. Finally, by carrying out single-objective factor optimization and multi-objective factor optimization, a set of preferred combinations of the factors is determined, and simulation tests are conducted to verify the results. The analysis results show that the RHT model of concrete material and the SPH algorithm can reasonably predict the shock wave propagation attenuation characteristics of multipoint charge explosions at different scaled bursting center distances as well as the induced damage and destruction of concrete. The main factors affecting the impact of the ground shock aggregation of explosive effect, in order of magnitude, are: scaled charge spacing, scaled detonation time difference and scaled active charge height. Under the conditions of the present test, the optimized detonation parameters are found as: the proportional charge spacing is 0.549 m/kg1/3, the proportional detonation time difference is 0.239 m/kg1/3, the proportional active charge height is 0. This set of parameters will result in the best ground shock aggregation effect, being up to 4.7 times the ground shock pressure produced by the same amount of single-point group charging.
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Key words:
- gray theory /
- aggregated explosion /
- concrete /
- degree of association /
- optimal design
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图 4 不同网格尺寸模拟得到的距装药中心不同距离处混凝土中的应力时间历程
Figure 4. Stress-time histories at different monitoring points in concrete with different distances away from the explosive charge center simulated by applying different mesh sizes
图 8 封闭爆炸时数值模拟结果与试验结果对比
Figure 8. Comparison of numerical simulation results and experimental ones during closed explosion
图 9 不同工况下测点的压力时程以及相应的数值模拟结果
Figure 9. Stress-time histories at the measured points under different test conditions and the corresponding numerically-simulated results
图 12 装药中心正下方应力时程曲线
Figure 12. Stress-time curves directly below the center of the charge
图 13 不同装药间距下装药下方比例爆心距0.191和1.620 m/kg1/3处的压力分布
Figure 13. Pressure distribution at the scaled distances to explosion center 0.191 and 1.620 m/kg1/3 below the charge center under different charge spacings
图 14 不同装药间距下峰值应力衰减曲线及放大倍数
Figure 14. Peak stress decay curves and their magnifications for different charge spacings
图 15 优化后起爆参数峰值应力衰减曲线及放大倍数
Figure 15. Optimized peak stress decay curve and amplification of detonation parameters
ρ0/(g·cm−3) A/GPa B/GPa R1 R2 ω D/(km·s−1) E0/GPa 1.63 373.77 3.7471 4.15 0.90 0.35 6.93 6.0 
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表 2 试验与数值模拟得到的弹坑尺寸
Table 2. Crater dimensions by test and numerical simulation
工况 弹坑的深度 弹坑的直径 模拟值/m 试验值/m 偏差/% 模拟值/m 试验值/m 偏差/% 七点爆炸 0.441 0.430 2.56 0.748 0.755 −0.93 单点爆炸 0.530 0.490 8.16 0.225 0.200 12.50
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表 3 试验与数值荷载峰值比较
Table 3. Comparison of experimental and numerical peak loads
工况 测点 荷载峰值 模拟值/MPa 试验值/MPa 偏差/% 七点爆炸 S1 29.7 29.2 1.71 S3 16.0 14.6 9.59 单点爆炸 S1 79.2 59.0 34.23 S4 3.9 3.7 5.41
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表 4 不同比例装药间距下拟合参数
Table 4. Fitting parameters for different proportions of charge spacing
Ω/(m∙kg−1/3) K N Ω/(m∙kg−1/3) K N 0 10.218 −1.810 0.549 14.843 −0.652 0.239 11.826 −1.597 0.812 11.218 −0.627 0.406 13.851 −1.169 0.955 10.220 −0.629
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表 5 控制因素和控制水平
Table 5. Control factors and level of control
控制因素 水平 1 2 3 (X1) Ω/(m∙kg−1/3) 0.406 0.549 0.812 (X2)Ψ/(m∙kg−1/3) 0 0.048 0.095 (X3)Γ/(m∙kg−1/3) 0 0.239 0.477
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表 6 试验设计L9(34)矩阵
Table 6. Experimental design L9(34) matrix
方案 水平组合 方案 水平组合 Ω Ψ Γ Ω Ψ Γ 1 1 1 1 6 2 3 2 2 1 2 2 7 3 1 2 3 1 3 3 8 3 2 3 4 2 1 3 9 3 3 1 5 2 2 1
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表 7 正交试验各序列区间值像
Table 7. Orthogonal test interval values for each sequence
工况 序列区间值像 x1(k) x2(k) x3(k) y1(k) y2(k) y3(k) 1 0.000 0.000 0.000 0.108 0.020 0.000 2 0.000 0.505 0.501 0.302 0.247 0.340 3 0.000 1.000 1.000 0.401 0.408 0.228 4 0.352 0.000 1.000 0.305 0.370 0.325 5 0.352 0.505 0.000 1.000 1.000 1.000 6 0.352 1.000 0.501 0.535 0.399 0.324 7 1.000 0.000 0.501 0.732 0.651 0.469 8 1.000 0.505 1.000 0.000 0.000 0.015 9 1.000 1.000 0.000 0.165 0.546 0.699
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表 8 3种因素在3种水平下就S3峰值应力的关联度系数和关联度
Table 8. Correlation coefficients and correlation of peak S3 stress at different levels of different factors
工况 关联度系数 Ω Ψ Γ 1 0.925 0.925 0.925 2 0.773 0.844 0.847 3 0.713 0.618 0.618 4 0.986 0.771 0.580 5 0.598 0.665 0.486 6 0.860 0.680 1.000 7 0.796 0.567 0.823 8 0.486 0.660 0.486 9 0.533 0.533 0.875 关联度 0.741 0.696 0.738
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表 9 多目标灰色关联度系数平均值
Table 9. Mean values of gray correlation coefficients for pairs of indicators
控制因素 平均灰色关联系数 1 2 3 Ω 0.816 0.829 0.601 Ψ 0.763 0.696 0.604 Γ 0.590 0.870 0.533
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