混凝土中柱形装药的爆炸破坏分区及应力波衰减规律

周鑫; 冯彬; 陈力

doi:10.11883/bzycj-2024-0350

混凝土中柱形装药的爆炸破坏分区及应力波衰减规律

doi: 10.11883/bzycj-2024-0350

东南大学爆炸安全防护教育部工程研究中心，江苏南京 211189

基金项目: 国家自然科学基金面上项目（52378487, 52378488）

详细信息

作者简介:
周　鑫（1996－　），男，博士研究生，zhouxin_0616@163.com

通讯作者:
冯　彬（1988－　），男，副研究员，fengbin.plaust@foxmail.com

中图分类号: O382
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- 被引次数: 0
出版历程
- 收稿日期: 2024-09-18
- 修回日期: 2024-12-19
- 网络出版日期: 2024-12-20

Study on failure zones and attenuation law of stress waves in concrete induced by cylindrical charge explosion

Engineering Research Center of Safety and Protection of Explosion & Impact of Ministry of Education, Southeast University, Nanjing 211189, Jiangsu, China

摘要

摘要: 为了探究柱形装药爆炸应力波在混凝土介质中的传播规律，基于Karagozian and Case concrete (KCC)本构模型和多物质ALE算法（multi-material ALE，MMALE）开展数值模拟研究。首先，通过与已有的试验数据进行对比，验证了本构模型参数和数值算法的适用性；在此基础上以峰值应力为准则，对装药周围混凝土介质的爆炸破坏分区进行划分，并讨论了各破坏分区中爆炸应力波的衰减规律；之后，分析了装药长径比对爆炸破坏分区和爆炸应力波传播规律的影响；最后，进一步考虑装药埋深的影响，并建立柱形装药爆炸应力波峰值应力计算公式。研究结果表明：各爆炸破坏分区中爆炸应力波衰减规律存在显著差异，与中远区（过渡区和破裂区）相比，装药近区（拟流体区和压碎区）衰减更快，另外，柱形装药长径比增加会加快法向峰值应力的衰减；并且建立的爆炸应力波峰值应力计算公式可以较为准确快速地计算出不同形状、不同埋深下柱形装药爆炸应力波的法向峰值应力。
- 混凝土 /
- 柱形装药 /
- 破坏分区 /
- 爆炸应力波 /
- 峰值应力
Abstract: In blast-resistant structural design for conventional weapons, previous studies on blast-induced stress waves in solid media have predominantly focused on soil and rock media (i.e., ground shock issues), whereas research on the propagation and attenuation laws of stress waves in concrete remains relatively limited. Based on the KCC constitutive model in conjunction with the multi-material ALE (MMALE) algorithm, the propagation laws of stress waves in concrete induced by cylindrical charge explosion were numerically investigated. Firstly, the applicability of the constitutive model parameters and numerical algorithm were validated by comparing the results with the existing experiments. Subsequently, the peak stress was employed as a criterion to delineate the explosive damage zones in the concrete surrounding the charge. Additionally, the attenuation laws of explosion stress waves in each damage zone were discussed. Finally, the effect of burial depth was taken into further considered, and a formula for calculating the peak stress in concrete induced by cylindrical charge explosion was established. It was found that the attenuation patterns of blast-induced stress waves differ significantly in each explosion failure zone. The stress waves in the near-field zone (quasi-fluid and crushing zones) demonstrates a more rapid attenuation rate compared to that in the mid-field zone (transition and fracture zones). Furthermore, an increase in the aspect ratio of the cylindrical charge leads to an acceleration in the attenuation of the normal peak stress. Moreover, the established formula for calculating the peak stress of blast-induced stress waves enables accurate and rapid determination of the normal peak stress generated by cylindrical charges with varying geometries and burial depths, which can be served as a valuable reference for blast-resistant design of concrete structures.
- concrete /
- cylindrical charges /
- failure zones /
- explosion stress waves /
- peak stress

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图 1 试验布置（单位：mm）

Figure 1. Schematic diagram of the experiment (Unit: mm)

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图 2 有限元模型

Figure 2. Finite element model

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图 3 网格收敛性分析

Figure 3. Mesh convergence analysis

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图 4 不同测点处的应力时程曲线

Figure 4. Stress-time curves at different measurement points

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图 5 有限元模型

Figure 5. Finite element model

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图 6 装药周围介质破坏分区

Figure 6. Failure zones of the surrounding medium around the charge

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图 7 环向应力时程曲线

Figure 7. Circumferential stress-time curves

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图 8 混凝土的损伤云图及破坏分区划分

Figure 8. Damage contour and the division of failure zones for concrete target

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图 9 柱形装药法向不同测点应力时程曲线

Figure 9. Normal stress-time curves at different measurement points for cylindrical charges

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图 10 峰值应力与比例距离关系

Figure 10. Relationship between peak stress and scaled distance

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图 11 各破坏分区竖向峰值应力与比例距离散点图

Figure 11. Scatter plot of vertical peak stress versus scaled distance for each failure zone

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图 12 破坏分区范围随着长径比的变化关系

Figure 12. Failure zone boundaries versus ratio of length to diameter

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图 13 装药底部及空腔壁处峰值应力变化趋势

Figure 13. Peak stress in guage1 and 2 versus ratio of length to diameter

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图 14 不同长径比条件下峰值应力与比例距离散点图

Figure 14. Scatter plot of peak stress versus scaled distance under different aspect ratios

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图 15 各破坏分区衰减系数k、衰减指数n与长径比的关系散点图

Figure 15. Scatter plot of attenuation coefficient k and attenuation index n versus aspect ratio for each failure zone

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图 16 数值模拟与式 (4)～(6) 计算结果对比

Figure 16. Comparison of stress peak values between numerical simulations and Eqs. (4)-(6)

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图 17 相对埋深及耦合系数简化模型示意图^[12]

Figure 17. Schematic diagram of relative burial depth and coupling coefficient f^[12]

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表 1 炸药本构模型及状态方程参数^[25]

Table 1. Parameters of constitutive model and EOS for explosive^[25]

ρ/(kg·m⁻³)	D/(m·s⁻¹)	p_CJ/GPa	A/GPa	B/GPa	ω	R₁	R₂	E/ (GJ·m⁻³)
1500	7450	22	625.3	23.29	0.28	5.25	1.60	8.56

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表 2 空气本构模型及状态方程参数^[26]

Table 2. Parameters of constitutive model and EOS for air^[26]

ρ/(kg·m⁻³)	C₀	C₁	C₂	C₃	C₄	C₅	C₆	E/(MJ·m⁻³)
1.2929	0	0	0	0	0	0.4	0	0.25

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表 3 第1组试验中各测点峰值应力的试验结果与数值模拟结果的对比

Table 3. Comparison of stress peak of tests with that of numerical simulation in the first group

测点试验值/GPa		试验平均值/GPa	数值模拟值/GPa	平均误差/%
gauge 1-1	gauge 1-4	10.261	8.476	17.40
11.156	9.366	10.261	8.476	17.40
gauge 1-3	gauge 1-6	1.316	1.134	13.83
1.248	1.384	1.316	1.134	13.83
gauge 1-2	gauge 1-5	0.492	0.531	7.93
0.518	0.466	0.492	0.531	7.93
注：平均误差=（试验平均值-数值模拟值）/平均值×100%

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表 4 混凝土自由场破坏分区边界尺寸及介质受力特征

Table 4. Concrete failure zone boundaries in a free field and stressed medium properties

破坏分区类型	边界尺寸/（mkg^1/3）	混凝土介质受力特征
近流体区	0.08～0.13	混凝土受强间断冲击波作用，其峰值应力远大于混凝土剪切强度，介质呈塑性流动状态
压碎区	0.13～0.17	爆炸应力值远大于混凝土抗压强度，介质被完全压碎
过渡区	0.17～0.46	混凝土介质受环向和径向压力共同作用，发生压剪破坏，裂隙呈网状分布
破裂区	0.46～1.0	混凝土介质主要受环向拉应力作用，发生拉伸破坏，形成径向裂隙
弹性区	≥ 1.0	介质未发生塑性变形，处于弹性状态

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表 5 不同长径比的柱形装药各破坏分区参数

Table 5. Parameters for different length-to-diameter ratios of cylindrical charges in each failure zone

l/d	分区	Z/(m/kg^1/3)	k	n	R²
2	近流体区	0.10～0.15	1.70×10⁻³	3.59	0.9937
	压碎区	0.15～0.18	6.05×10⁻⁴	3.96	0.9862
	过渡区	0.18～0.44	2.03×10⁻²	1.98	0.9943
	破裂区	0.44～1.00	3.28×10⁻²	1.47	0.9991
4	近流体区	0.14～0.17	1.82×10⁻⁴	5.25	0.9945
	压碎区	0.17～0.20	1.69×10⁻⁵	6.59	0.9780
	过渡区	0.20～0.42	1.62×10⁻²	2.24	0.9891
	破裂区	0.42～1.00	3.16×10⁻²	1.52	0.9991
6	近流体区	0.17～0.20	4.88×10⁻⁵	6.61	0.9964
	压碎区	0.20～0.22	1.34×10⁻⁶	8.83	0.9705
	过渡区	0.22～0.40	1.16×10⁻²	2.66	0.9826
	破裂区	0.40～1.00	3.05×10⁻²	1.59	0.9985
8	近流体区	0.20～0.23	6.66×10⁻⁶	8.49	0.9897
	压碎区	0.23～0.25	5.39×10⁻⁷	10.15	0.9773
	过渡区	0.25～0.40	9.30×10⁻³	2.97	0.9783
	破裂区	0.40～1.00	2.85×10⁻²	1.67	0.9975

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