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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在自然灾害救援和非战争行动中, 经常面临对大块度障碍物快速破除的难题。普通民用爆破中通常采取先机械钻孔、后装药起爆的方法进行施工, 但在缺少时间、机械设备、电力和人员等条件下, 一般方法无法短时内快速清除这些大块度障碍, 常常造成救援目标生命及财产的重大损失。考虑到应急保障的高时效性, 采用串联装药技术更有效[1]。张先锋等[2]、王树有等[3]、曾必强等[4]和涂候杰等[5]分别对串联战斗部前级爆轰对后级的影响进行了数值模拟分析和实验研究, 王成等[6]对同口径串联装药前后级成型关系进行了实验研究。传统的破-爆型串联战斗部前级聚能开孔装药能力有限, 在大块度障碍物破除应用中效果不理想。因此, 本文中根据在坚硬目标上开孔的需要, 提出一种新式破-破型串联爆炸成型弹丸(explosively formed projectile, EFP)聚能装药结构作为多级串联战斗部的前级开孔装药, 并对串联EFP装药隔爆结构和装药前后级延时匹配进行优化设计; 利用有限元程序LS-DYNA对不同起爆延时条件下串联EFP装药侵彻进行数值计算, 并进行实验验证。
1. 串联装药结构
1.1 单级EFP装药选择
本文中选择前期优化设计[7]得到的Ø65 mm球缺型变壁厚EFP装药结构方案。装药结构参数为:炸药采用JH-2, 其密度为1 700 kg/m3, 装药长径比为1.0;药型罩采用紫铜材料, 罩顶厚2.1 mm, 罩内表面曲率半径为67 mm, 外表面曲率半径为62 mm。
1.2 串联EFP关键技术
为确保精确控制两级EFP装药的起爆时间, 采用本课题专门设计的精确延时起爆控制器, 设定延时间隔精度为0.1 μs, 可通过专用的应用软件在0~200 μs区间任意设定延时, 图 1是2路起爆控制信号输出时示波器采集到的触发信号波形。
1.3 隔爆体设计原则
本研究串联EFP采用逆序起爆方式, 前级装药爆炸后产生的爆轰产物和空气冲击波不可避免地作用在后级装药上, 引起后级EFP形状和性能的改变, 从而改变后级EFP的侵彻性能。因此要设计一种简单的隔爆结构, 降低前后级之间的影响。本研究的隔爆结构中选用的聚氨酯泡沫材料是一种密度小、隔爆性能好的抗冲击波材料, 广泛应用于国防、军事领域[8]。
2. 数值模拟分析
2.1 串联EFP数值模型
为了分析隔爆体及起爆延时对串联EFP装药成型性能的影响, 利用有限元软件LS-DYNA3D对其成型过程进行数值模拟, 串联装药模型如图 2所示。模型涉及聚能装药成型和侵彻2个部分, 采用流-固耦合算法来分析此类情况更贴近实际。模型中, 炸药、药型罩、隔爆体和空气等介质均采用Euler算法, 靶板则采用Lagrange算法。串联EFP装药为8701炸药, 采用高能炸药材料模型和JWL状态方程描述; 药型罩材料为军用紫铜, 用Grüneisen状态方程和Johnson-Cook本构模型描述[9-10]; 隔爆体为聚氨酯泡沫, 用Grüneisen状态方程和Elastic_Plastic_Hydro本构模型描述, 各材料状态方程参数[11-12]如表 1~3所示, 其中:ρ为密度, v为爆速, pCJ为炸药的C-J爆压, E0为材料的初始内能, A、B、R1、R2和ω为炸药的材料常数, C为材料的us-up截距, S1、S2和S3为斜度系数, γ0为材料的Grüneisen系数, a为γ0的一阶体积修正。
表 1 JH-2炸药计算参数Table 1. Computational parameters for JH-2ρ/(g·cm-3) v/(m·s-1) pCJ/GPa A/GPa E0/(J·m-3) B R1 R2 ω 1.70 8 400 30 56.4 10.0 6.801 4.1 1.3 0.36 表 2 紫铜和聚氨酯泡沫计算参数Table 2. Computational parameters for copper linerρ/(g·cm-3) C/(m·s-1) S1 S2 S3 γ0 a E0 8.96 4 750 3.8 2.74 0.125 1.346 0.34 0.0 表 3 聚氨酯泡沫计算参数Table 3. Computational parameters for polyurethane foamρ/(g·cm-3) C/(m·s-1) S1 S2 S3 γ0 a E0 0.05 886 0.78 0.0 0.0 1.55 0.00 0.0 2.2 不同炸高条件下单级EFP侵彻过程分析
要充分发挥两级串联EFP装药的侵彻能力, 首先需要确定装药的有利炸高。如果炸高太小, EFP弹丸还未完全成型, 其速度和长径比仍在快速变化中, 侵彻深度和穿孔直径等侵彻效果随炸高变化而发生较大改变。但炸高达到一定程度后, EFP成型性能已经基本稳定时, 侵彻效果变化逐渐减小。文中选取了6种不同炸高进行了数值模拟和实验, 结果如图 3所示, 其中:H为炸高, D为装药直径。
对比图 3中6种炸高条件下钢靶剖面图得出:在炸高与装药直径比小于2.8时, EFP侵彻钢靶孔径较大, 但EFP未得到有效拉伸, 侵彻深度不大; 随着炸高的增加, 侵彻深度逐渐增加, 同时孔径逐渐减小; 在炸高与装药直径比大于3.2时, 炸高增加, 侵彻深度与孔径基本不变。表 4为不同炸高下EPF侵彻钢靶的模拟和实验结果, 其中h为侵彻深度, d为侵彻孔径。分析表 4中的数据发现, 数值模拟与实验结果在侵彻深度和孔径大小上吻合较好, 误差在5%以内, 说明数值模拟结果较贴近实际, 为后面串联装药模拟提供了一种可行的方法。
表 4 EFP侵彻钢靶数值模拟与实验数据Table 4. Simulational and experimental results of EFP penetrating steel targetsH/mm h/D d/D 模拟值 实验值 模拟值 实验值 150 0.73 0.74 0.557 0.563 180 0.80 0.78 0.525 0.530 210 0.85 0.86 0.498 0.495 240 0.89 0.88 0.477 0.472 270 0.90 0.89 0.460 0.454 300 0.90 0.90 0.455 0.451 2.3 不同隔爆体形状串联EFP成型过程数值模拟
隔爆效果不仅与材料性能有关, 隔爆体的形状对后级装药成型影的响也十分巨大。文中选取了3种不同结构的隔爆体进行分析。图 4为圆柱形隔爆体、锥口向上隔爆体和锥口向下3种条件下串联EFP装药200 μs时刻后级EFP成型状态。通过对比图 4中的3种后级EFP形态, 发现隔爆体结构的不同对减少前级爆轰对后级成型的影响差异很大。采用圆柱形隔爆体时后级EFP基本成型, 但头尾连续性差, EFP侵彻能力大大降低; 采用圆柱底部挖出一个锥形空腔且锥口向上的隔爆体, 隔爆效果差, 后级弹丸基本无翻转, 后级装药侵彻能力基本消失; 锥口向下的隔爆体, 隔爆效果较理想, 可作为串联EFP的隔爆结构基本形状, 后级EFP成型较好, 但在前级爆轰场影响下, EFP长径比增大, 需要进一步优化前后级起爆时间, 来提高后级EFP的成型效果。
图 4 不同隔爆体200 μs时刻后级EFP形态Figure 4. Shapes of the postpositive EFP charge at 200 μs with different explosion-proof bodies2.4 不同延时串联EFP侵彻过程数值模拟分析
串联EFP前后级延时起爆时间Δt对后级EFP的成型和侵彻性能影响很大[8]。在两级装药间距一定的情况下, 合理控制延时起爆时间Δt, 使后级EFP受前级装药爆轰场影响最小, 才能最大限度地保持后级EFP装药的成型性能。分别对5种不同延时条件下串联EFP侵彻靶板进行数值模拟, 结果见表 5。
表 5 串联EFP装药侵彻数值模拟结果Table 5. Simulation results of tandem EFP penetrationΔt/μs h/mm h/D d/mm d/D 0 92 1.415 22.2 0.341 10 103 1.584 21.6 0.332 20 115 1.769 21.4 0.329 25 104 1.600 21.7 0.327 30 98 1.507 21.3 0.334 图 5给出了侵彻深度和侵彻孔径随起爆延时的变化关系。分析图 5中孔径和孔深的变化规律可以发现, 随着前后级延时起爆时间的增加, 后级EFP的侵彻深度先增大后快速减小, 说明前级爆轰场到达后级装药时, 会严重影响后级EFP的成型。所以, 该串联结构较为合理的延时为20 μs。图 6为同时起爆和延时20 μs的数值模拟侵彻结果。
图 5 开孔深度和直径随起爆延时的变化Figure 5. Variation of penetration depth and aperture with delay time3. 串联EFP隔爆结构实验研究
3.1 不同隔爆形体状串联EFP侵彻实验
根据前期研究[1]得到的隔爆体形状对串联EFP装药侵彻性能的影响规律, 进行6发串联EFP侵彻的验证性实验。实验分3组, 分别采用圆柱形、锥口向上和锥口向下3种隔爆体, 每组进行2发实验。图 7为3种不同条件下EFP的侵彻性能实验结果。
图 7 不同隔爆体串联EFP侵彻结果Figure 7. Penetration results of tandem EFPs with different explosion-proof bodies表 6给出了串联装药对靶板的侵彻结果, 通过对比可以发现, 同时起爆条件下, 锥口向下的隔爆体侵彻深度明显优于其他2种结构。但后级侵彻的开孔孔径较小, 难以满足后级爆破子弹随进要求, 需进一步优化。
表 6 串联EFP装药侵彻钢靶实验结果Table 6. Experimental results of tandem EFPs penetrating steel targets隔爆结构 h/mm d/mm 圆柱形 82 15.2 锥口向上 60 16.6 锥口向下 98 16.3 3.2 不同延时条件下串联EFP侵彻钢靶实验
图 8为实验设置图。前级装药炸高取210 mm, 装药间距150 mm条件下, 采用中心起爆方式, 使用8#电雷管同时起爆两级装药, 分别对延时0、10、20、25和30 μs等5种情况进行侵彻靶板分别进行2发实验, 结果依次记录为A1~A10。为对比优化后的侵彻性能, 同时进行2组分2次单独侵彻实验作为参照, 结果记录为B1和B2。侵彻结果显示串联EFP开孔形状前后基本一致。后级EFP受到前级装药爆轰场的影响, 速度和长径比都不可避免有所下降, 开孔直径比前级EFP小。
表 7给出了不同延时条件下的侵彻深度和最小侵彻孔径的实验结果。由表 7可以看出:随着延时的增加, 后级EFP受到前级爆轰场影响, 形状变得更加细长, 侵彻的孔径逐渐变小; 而穿孔深度先逐渐增加, 随后逐渐减小。这说明起爆时间间隔太大, 前级爆轰场到达后级装药后, 会严重影响后级EFP的成型, 大大降低了后级EFP的速度。将表 7与表 5进行比较, 可以看出两者最大仅相差3.7%, 可见实验结果与数值模拟结果吻合较好。
表 7 串联EFP装药侵彻钢靶结果Table 7. Experimental results of tandem EFPs penetrating steel targets编号 Δt/μs h/mm d/mm A1 0 94 21.4 A2 0 95 21.3 A3 10 105 21.0 A4 10 102 21.2 A5 20 117 20.6 A6 20 115 20.8 A7 25 107 20.4 A8 25 108 20.3 A9 30 100 20.3 A10 30 102 20.2 B1 121 21.6 B2 119 21.8 图 9所示靶板, 依次为分2次侵彻、延时0和延时20 μs侵彻实验结果。可以看出:同时起爆(Δt=0)时, 后级EFP长径比和速度受影响较大, 侵彻孔径较分2次侵彻时减小0.4 mm, 后级EFP侵彻深度只有分2次侵彻时第2次侵彻深度的58.9%, 侵彻效果大大降低。延时起爆20 μs时, 侵彻孔径较分2次侵彻时减小1 mm, 两级整体侵彻深度为分2次侵彻时的96.7%, 这体现了延时起爆对后级EFP侵彻性能的重要性。
图 9 不同起爆延时下串联EFP装药侵彻钢靶实验结果Figure 9. Tandem EFP charge penetrating steel targets with different delay time4. 结论
(1) 在已有的研究成果基础上, 分析了隔爆体形状和前后级装药延时对串联EFP侵彻能力的影响, 得到了较合理的串联装药结构。
(2) 通过数值模拟和实验研究, 对串联EFP装药隔爆结构形状和延时匹配进行了比较分析, 延时起爆20 μs时, 串联侵彻深度为分2次侵彻的96.7%, 比同时起爆侵彻深度提高了约22.8%, 大大提高了后级装药的利用效率。这可为下一步多级串联装药研究提供依据。
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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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1. Shuai Qin，Hao Liu，Jianhui Wang，Qiang Zhao，Lei Zhang. Physics-data coupling-driven method to predict the penetration depth into concrete targets. Theoretical & Applied Mechanics Letters. 2024(03): 184-192 . 
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