地下爆炸耦合系数与填塞系数确定方法

张效晗; 徐天涵; 王明洋

doi:10.11883/bzycj-2025-0401

地下爆炸耦合系数与填塞系数确定方法

doi: 10.11883/bzycj-2025-0401

张效晗^{1, 2,},
徐天涵^3, ,,
王明洋³

1.
上海市地下空间设计研究总院有限公司，上海 200001
2.
南京理工大学机械工程学院工程安全防护技术研究所，江苏南京 210094
3.
陆军工程大学爆炸冲击防灾减灾全国重点实验室，江苏南京 210007

基金项目: 国家自然科学基金（52509159）；国家重点研发计划（2024YFF0508204）

详细信息

作者简介:
张效晗（1987－　），女，博士研究生，高级工程师，zhangxiaohan@suadi.com.cn

通讯作者:
徐天涵（1995－　），男，博士，副教授，martinxu41@qq.com

中图分类号: O389
计量
- 文章访问数: 130
- HTML全文浏览量: 8
- PDF下载量: 49
- 被引次数: 0
出版历程
- 收稿日期: 2025-12-10
- 修回日期: 2026-05-26
- 网络出版日期: 2026-06-09

Methods for determining the coupling coefficient and stemming coefficient of underground explosions

ZHANG Xiaohan^{1, 2
,},
XU Tianhan^{3
, ,},
WANG Mingyang³

1.
Shanghai Underground Space Design and Research Institute Co., Ltd., Shanghai 200001, China
2.
Institute of Engineering Safety Protection Technology, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
3.
State Key Laboratory of Explosion and Impact and Disaster Prevention and Mitigation, Army Engineering University of PLA, Nanjing 210007, Jiangsu, China

摘要

摘要: 耦合系数与填塞系数广泛应用于地下爆炸地冲击大小预测及爆炸破坏范围评估，随着埋深增加，爆炸地冲击耦合机制发生变化，不同耦合系数呈现不同演化规律。系统总结了地下爆炸耦合系数和填塞系数的试验与理论研究成果，介绍了常用耦合系数类型及换算关系，分析了现有试验中不同耦合系数及不同介质中耦合系数随埋深的变化规律，讨论了耦合系数计算方法及临界埋深确定方法，对比了不同介质中的等效当量系数和填塞系数，并对目前研究中尚有待解决的问题和下一步的研究方向进行了展望。
- 地下爆炸 /
- 耦合系数 /
- 填塞系数 /
- 地冲击 /
- 临界埋深
Abstract: Coupling coefficients and stemming coefficients are essential for predicting ground shock magnitude and damage zones from underground explosions, yet their variation with burial depth and dependence on media and explosion types remain insufficiently compared. Experimental and theoretical methods for determining these coefficients in concrete, rock, and soil under both chemical and nuclear explosions were systematically reviewed. Based on collected data from published tests, definitions of different coupling coefficients (energy coupling, ground shock parameter coupling, equivalent yield, and stemming coefficients) were clarified, and conversion relationships among them were derived using energy conservation and wave attenuation principles. The critical burial depth for full coupling was analyzed separately for peak quantities (e.g., peak stress, particle velocity) and integral quantities (e.g., impulse, surface vibration). Experimental results show that peak quantities reach full coupling at a depth approximately equal to the contained explosion cavity radius, which is much shallower than the critical depth for contained explosions. In contrast, impulse and ground motion require depths close to the contained explosion threshold. The coupling energy is proportional to the volume of the damaged zone, and the evolution of coupling coefficients with scaled depth of burial follows a Boltzmann function, requiring only two parameters to define the entire curve. For chemical explosions, the fully coupled equivalent yield coefficient (relative to contained explosions) in concrete, limestone, and soils was quantified, with stemming coefficients ranging from 1.4~1.8 in rocks and 2.4~2.6 in soils. It is concluded that different ground shock parameters exhibit distinct coupling behaviors, challenging the assumption of a universal coupling coefficient. Proposed empirical formulas provide conservative estimates for engineering design, while the underlying mechanisms of free-surface unloading require further quantitative investigation.
- underground explosion /
- coupling coefficient /
- stemming coefficient /
- ground shock /
- critical burial depth

HTML全文

图 1 成坑形态随爆炸埋深的变化

Figure 1. Variation of crater shapes with explosion burial depth

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图 2 地下爆炸破坏区演化示意图

Figure 2. Schematic diagram of the evolution of damage zones of underground explosion

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图 3 混凝土中等效当量系数^[5]

Figure 3. Equivalent coefficients in concrete^[5]

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图 4 靶体破坏现象^[11]

Figure 4. Phenomena of target destruction^[11]

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图 5 石灰岩中等效当量系数^[6]

Figure 5. Equivalent coefficient in limestone^[6]

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图 6 砂质黏土中应力等效当量系数^[8]

Figure 6. Equivalent coefficient in sandy clay^[8]

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图 7 黄土中应力冲量耦合系数^[19]

Figure 7. Coupling coefficient of stress impluse in loess^[19]

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图 8 爆炸成坑现象^[19]

Figure 8. Explosive craters of the experiments^[19]

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图 9 黄土中爆炸成坑尺寸^[10]

Figure 9. Crater sizes in loess^[10]

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图 10 黄土中填塞系数^[10]

Figure 10. Stemming coefficient in loess^[10]

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图 11 黏土中应力耦合系数与填塞系数^[12]

Figure 11. η_p,σ and η_m in clay^[12]

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图 12 黏土中爆炸现象^[12]

Figure 12. Craters and cavities in clay^[12]

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图 13 TM5-855-1中的地冲击参数耦合系数^[15]

Figure 13. η_p in TM5-855-1^[15]

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图 14 美国地下核爆能量耦合系数

Figure 14. η_e of underground nuclear explosions of USA

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图 15 俄罗斯地下核爆能量耦合系数^[4]

Figure 15. η_e of underground nuclear explosions of Russia^[4]

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图 16 地下核爆地表震动速度耦合系数^[4]

Figure 16. Coupling coefficient of the ground vibration velocity of underground nuclear explosions^[4]

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图 17 与美俄耦合系数曲线对比

Figure 17. Comparison between the Boltzmann curve and the curves of USA and Russia

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图 18 不同介质中等效当量系数对比

Figure 18. Comparisons of η_Q in different media

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图 19 不同介质中填塞系数对比

Figure 19. Comparisons of η_m in different media

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表 1 黏土中试验结果

Table 1. Experimental results in clay

装药埋深/(m·kg^−1/3) 爆心下方压缩比例半径/(m·kg^−1/3)

−0.056 0.179

0 0.184

0.14 0.289

0.37 0.340

0.55 0.453

1.19 0.478

1.46 0.479

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