柱形装药接触爆炸作用下钢纤维混凝土靶成坑效应预测模型

杨石刚; 王彬刚; 许继恒; 方秦; 杨亚; 罗泽

doi:10.11883/bzycj-2025-0263

柱形装药接触爆炸作用下钢纤维混凝土靶成坑效应预测模型

doi: 10.11883/bzycj-2025-0263

杨石刚^1,,
王彬刚^1, ,,
许继恒¹,
方秦¹,
杨亚²,
罗泽³

1.
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 210094
2.
中国人民解放军 63983部队，江苏无锡 214000
3.
中国人民解放军 32573部队，广东东莞 523000

详细信息

作者简介:
杨石刚（1985－　），男，博士，副教授，youngshg@126.com

通讯作者:
王彬刚（1996－　），男，博士研究生，2575667171@qq.com

中图分类号: O389
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- 文章访问数: 354
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- 被引次数: 0
出版历程
- 收稿日期: 2025-08-25
- 修回日期: 2026-01-22
- 网络出版日期: 2026-01-30

Prediction model of crater damage effect of steel fiber reinforced concrete target under contact explosion of cylinder charge

1.
State Key Laboratory of Explosion&Impact and Disaster Prevention&Mitigation, Army Engineering University of PLA, Nanjing 210094, Jiangsu, China
2.
Unit of 63983 of the People’s Liberation Army of China, Wuxi 214000, Jiangsu, China
3.
Unit of 32573 of the People’s Liberation Army of China, Dongguan 523000, Guangdong, China

摘要

摘要: 为评估柱形装药接触爆炸对钢纤维钢筋混凝土（steel fiber reinforced concrete, SFRC）结构的成坑效应，采用光滑粒子伽辽金与结构化任意拉格朗日-欧拉流固耦合算法建立了SFRC靶体数值模型，研究了不同装药量Q和长径比l/d联合作用下SFRC靶体的破坏模式和损伤程度，基于接触爆炸理论与量纲分析，引入爆坑系数K₁与 K₂构建了爆坑直径D与深度H随有效装药量Q_e变化的预测模型。结果表明：不同装药量和长径比联合作用下，SFRC靶体主要呈爆炸成坑破坏。不同装药量情况下，当l/d由1增大至5时，爆坑直径D与深度H均减小了约50%。在Q_e小于16 kg范围内，K₁与$ \sqrt{{K}_{2}} $随有效装药量呈幂函数衰减，而D与H则随有效装药量呈幂函数增长。在相同Q_e条件下，成坑效应更集中于爆坑直径的扩展。构建的预测模型可对不同强度等级与有效装药量下SFRC的爆坑尺寸进行快速且较为准确的计算，为SFRC结构的抗爆设计提供理论依据。
- 钢纤维钢筋混凝土 /
- 柱形装药 /
- 接触爆炸 /
- 爆坑深度 /
- 爆坑直径
Abstract: To evaluate the crater damage effect of cylinder charge contact explosion on steel fiber reinforced concrete (SFRC) structures, a numerical model of an SFRC target was developed by the using the smooth particle Galerkin method and a structured arbitrary Lagrange-Euler (SPG-S-ALE) fluid-structure interaction algorithm. The failure modes and damage of the SFRC target under different charge mass Q and length-to-diameter ratios l/d were investigated. Based on contact explosion theory and dimensional analysis, cratering coefficients K₁ and K₂ were introduced to develop predictive models for the crater diameter D and depth H as functions of the effective charge mass Qₑ. The results indicate that under the combined effects of charge mass and length-to-to-diameter ratio, the primary failure mode of the SFRC targets is cratering damage. Under constant charge mass conditions, as the l/d ratio increases from 1 to 5, both the crater diameter D and depth H decrease by approximately 50%. Within the range of effective charge Qₑ less than 16 kg, the K₁ and$ \sqrt{{K}_{2}} $ exhibit a power-law decay with increasing effective charge mass, while the crater diameter D and depth H show a power-law growth. For a given effective charge mass Qₑ, the cratering effect is more concentrated on the expansion of the crater diameter. The developed predictive model allows for rapid and reasonably accurate calculation of crater dimensions in SFRC with different strength grades and effective charge mass, providing a theoretical basis for the blast-resistant design of SFRC structures.
- steel fiber reinforced concrete /
- cylinder charge /
- contact explosion /
- crater diameter /
- crater depth

HTML全文

图 1 SFRC靶体有限元模型

Figure 1. Finite element model of the target of SFRC

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图 2 网格尺寸敏感性分析

Figure 2. Mesh size sensitivity analysis

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图 3 试验装置^[11]

Figure 3. Test equipment^[11]

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图 4 有限元模型

Figure 4. Finite element model

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图 5 SFRC靶体试验结果与数值模拟结果

Figure 5. Test results and numerical results of SFRC target

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图 6 Q=11 kg、l/d=1时SFRC 靶应力传播过程

Figure 6. Evaluation process of Von Mises stress distribution in the SFRC target under Q=11 kg and l/d=1

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图 7 Q=11 kg、l/d=1时SFRC靶损伤发展过程

Figure 7. Damage evaluation in the SFRC target under Q=11 kg and l/d=1

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图 8 不同装药量Q和长径比l/d下SFRC靶爆坑尺寸对比

Figure 8. Comparison of diameter and depth of SFRC under different Q and l/d

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图 9 爆坑系数拟合结果

Figure 9. Fitting results of crater coefficient

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图 10 爆坑尺寸计算结果

Figure 10. Calculated results of crater dimension

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表 1 CF60 钢纤维混凝土K＆C模型参数^[21]

Table 1. Parameters of K＆C model for CF60 steel fiber concrete^[21]

ρ/(kg·m⁻³)	f_c/MPa	v	f_t/MPa	RSIZE	UFC	a₀	a_0y	a_0f
2440	65	0.24	4.95	39.37	1.45×10⁻⁴	−6.5×10⁷	1.703×10⁷	0

a₁	a_1y	a_1f	a₂	a_2y	a_2f	b₁	b₂	b₃
0.481	0.726	0.476	1.57×10⁻⁹	4.77×10⁻⁹	2.31×10⁻⁹	0.75	0.2	0.018
注：ρ为密度；f_c为抗压强度，f_t为抗拉强度，v为泊松比，RSIZE为长度单位转换因子，UFC为应力单位转换因子，a₀、a_0y、a_0f、a₁、a_1y、a_1f、a₂、a_2y、a_2f为强度面参数，b₁、b₂、b₃为损伤参数。

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表 2 钢筋和钢板材料参数^[21]

Table 2. Parameters of steel^[21]

材料	ρ/(kg·m⁻³)	E/GPa	v	σ_y/MPa
HRB400钢筋	7 850	205	0.29	400
Q235钢板	7 850	210	0.3	310
注：E为弹性模量，σ_y为屈服强度。

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表 3 空气及状态方程参数^[24]

Table 3. Air and equation of state parameters^[24]

ρ/(kg·m⁻³)	C₀	C₁	C₂	C₃	C₄	C₅	C₆	E₀/(GJ·m⁻³)	V₀
1.29	0	0	0	0	0.4	0	0	250	1
注：C₀～C₆为状态方程系数，E₀为初始内能，V₀为初始相对体积。

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表 4 炸药及状态方程参数^[24]

Table 4. Explosive and equation of state parameters^[24]

ρ/(kg·m⁻³)	D₁/(m·s⁻¹)	p/GPa	A/GPa	B/MPa	R₁	R₂	ω	E₀/(GJ·m⁻³)
1 630	6 930	21	373	3 747	4.15	0.9	0.35	7
注：A、B、R₁、R₂、ω为炸药参数，E₀为初始内能，p为爆轰压力，D₁为爆速。

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表 5 SFRC靶K＆C模型参数

Table 5. Parameters of K＆C model for SFRC target

ρ/(kg·m⁻³)	f_c/MPa	v	f_t/MPa	RSIZE	UFC	a₀	a_0y	a_0f
2440	107	0.24	9.3	39.37	1.45×10⁻⁴	−1.07×10⁸	3.17×10⁷	0

a₁	a_1y	a_1f	a₂	a_2y	a_2f	b₁	b₂	b₃
0.533	0.827	0.527	7.34×10⁻¹⁰	2.23×10⁻⁹	1.08×10⁻⁹	1.6	−2	1.15

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表 6 不同装药量与长径比作用下SFRC靶体破坏形态

Table 6. Failure modes of SFRC targets under varying Q and l/d

l/d	SFRC靶体破坏形态
l/d	Q =1 kg	Q =3 kg	Q =5 kg	Q =7 kg	Q =9 kg	Q =11 kg
1
2
3
4
5

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参考文献(33)

[1]	LIU J, LI J, FANG J G, et al. Investigation of ultra-high performance concrete slabs under contact explosions with a calibrated K&C model [J]. Engineering Structures, 2022, 255: 113958. DOI: 10.1016/j.engstruct.2022.113958.
[2]	PENG Y, WU C Q, LI J, et al. Mesoscale analysis on ultra-high performance steel fibre reinforced concrete slabs under contact explosions [J]. Composite Structures, 2019, 228: 111322. DOI: 10.1016/j.compstruct.2019.111322.
[3]	GRISARO H Y, BENAMOU D, MITELMAN A. Field tests of fiber reinforced concrete slabs subjected to close-in and contact detonations of high explosives [J]. International Journal of Impact Engineering, 2022, 162: 104136. DOI: 10.1016/j.ijimpeng.2021.104136.
[4]	郑全平, 牛小玲, 汪剑辉, 等. 不同钢纤维掺量C30 RC板爆炸震塌试验研究 [J]. 防护工程, 2013, 35(1): 16–20. DENG Q P, NIU X L, WANG J H, et al. Experimental investigation into explosion spalling of C30 RC plates with different steel fiber content [J]. Protective Engineering, 2013, 35(1): 16–20.
[5]	李晓军, 郑全平, 杨益. 钢纤维钢筋混凝土板爆炸局部破坏效应 [J]. 爆炸与冲击, 2009, 29(4): 385–389. DOI: 10.3321/j.issn:1001-1455.2009.04.009. LI X J, ZHENG Q P, YANG Y. Local damage effects of steel fiber reinforced concrete plates subjected to contact explosion [J]. Explosion and Shock Waves, 2009, 29(4): 385–389. DOI: 10.3321/j.issn:1001-1455.2009.04.009.
[6]	ZHAO X H, JIANG G, YANG L, et al. Experimental study on the damage characteristics of steel fiber reinforced concrete slabs attacked by chloride ion under contact explosion [J]. Applied Ocean Research, 2024, 153: 104270. DOI: 10.1016/j.apor.2024.104270.
[7]	魏久淇, 李磊, 王世合, 等. 超高性能混凝土临空板接触爆炸破坏效应实验研究 [J]. 爆炸与冲击, 2022, 42(4): 042201. DOI: 10.11883/bzycj-2021-0174. WEI J Q, LI L, WANG S H, et al. Experimental study on local damage effect of ultra-high performance concrete slabs under contact explosion [J]. Explosion and Shock Waves, 2022, 42(4): 042201. DOI: 10.11883/bzycj-2021-0174.
[8]	LI J, WU C Q, HAO H, et al. Experimental investigation of ultra-high performance concrete slabs under contact explosions [J]. International Journal of Impact Engineering, 2016, 93: 62–75. DOI: 10.1016/j.ijimpeng.2016.02.007.
[9]	ZHAO X H, SUN J S, ZHAO H N, et al. Experimental and mesoscopic modeling numerical researches on steel fiber reinforced concrete slabs under contact explosion [J]. Structures, 2024, 61: 106114. DOI: 10.1016/j.istruc.2024.106114.
[10]	LUCCIONI B, ISLA F, CODINA R, et al. Effect of steel fibers on static and blast response of high strength concrete [J]. International Journal of Impact Engineering, 2017, 107: 23–37. DOI: 10.1016/j.ijimpeng.2017.04.027.
[11]	YANG D P, ZHANG B, LIU G J. Experimental study on spall resistance of steel-fiber reinforced concrete slab subjected to explosion [J]. International Journal of Concrete Structures and Materials, 2021, 15(1): 23. DOI: 10.1186/s40069-021-00459-8.
[12]	张永亮. 钢纤维混凝土材料的抗爆抗侵彻性能研究及应力波演化 [D]. 合肥: 中国科学技术大学, 2018. ZHANG Y L. Study on anti explosion and anti penetration properties of SFRC and evolution of stress wave [D]. Hefei: University of Science and Technology of China, 2018.
[13]	卢康道, 孙伟. 钢纤维增强混凝土抗爆性能的研究 [J]. 混凝土与水泥制品, 2002(5): 32–34. DOI: 10.19761/j.1000-4637.2002.05.011. LU K D, SUN W. Study on the resistance of fiber reinforced concrete to exploding [J]. China Concrete and Cement Products, 2002(5): 32–34. DOI: 10.19761/j.1000-4637.2002.05.011.
[14]	LUCCIONI B, ISLA F, CODINA R, et al. Experimental and numerical analysis of blast response of High Strength Fiber Reinforced Concrete slabs [J]. Engineering Structures, 2018, 175: 113–122. DOI: 10.1016/j.engstruct.2018.08.016.
[15]	LIN S H, LIU J, LIU C, et al. Triaxial compressive behaviour of ultra-high performance geopolymer concrete (UHPGC) and its applications in contact explosion and projectile impact analysis [J]. Construction and Building Materials, 2024, 449: 138394. DOI: 10.1016/j.conbuildmat.2024.138394.
[16]	GAN L, ZONG Z H, GAO C, et al. Influence of shape of cuboid explosives on response of plates subjected to blast loads [J]. Thin-Walled Structures, 2022, 174: 109077. DOI: 10.1016/j.tws.2022.109077.
[17]	郝礼楷, 顾文彬, 邹绍昕, 等. 空气中集团装药对混凝土墩接触爆炸毁伤研究 [J]. 兵器装备工程学报, 2022, 43(5): 97–102. DOI: 10.11809/bqzbgcxb2022.05.016. HAO L K, GU W B, ZOU S X, et al. Damage study of concrete obstacle caused by air contact explosion of group charge [J]. Journal of Ordnance Equipment Engineering, 2022, 43(5): 97–102. DOI: 10.11809/bqzbgcxb2022.05.016.
[18]	王琰, 蒋海燕, 韩璐, 等. 柱形装药形状对加筋板架动态响应的影响研究 [J]. 火工品, 2024(3): 77–83. DOI: 10.3969/j.issn.1003-1480.2024.03.013. WANG Y, JIANG H Y, HAN L, et al. Study on dynamic response of stiffened plate frame by cylindrical charge shape [J]. Initiators & Pyrotechnics, 2024(3): 77–83. DOI: 10.3969/j.issn.1003-1480.2024.03.013.
[19]	张强, 余曜, 迟德建, 等. 柱形装药接触爆炸条件下对钢筋混凝土板的毁伤规律研究 [J]. 空天防御, 2020, 3(2): 16–23. DOI: 10.3969/j.issn.2096-4641.2020.02.003. ZHANG Q, YU Y, CHI D J, et al. Study on the damage effect of cylindrical charge on reinforced concrete slabs [J]. Air & Space Defense, 2020, 3(2): 16–23. DOI: 10.3969/j.issn.2096-4641.2020.02.003.
[20]	方秦, 柳锦春. 地下防护结构 [M]. 北京: 中国水利水电出版社, 2010.
[21]	杨石刚, 罗泽, 许继恒, 等. 侵彻爆炸作用下钢纤维混凝土结构的破坏模式 [J]. 爆炸与冲击, 2024, 44(1): 015102. DOI: 10.11883/bzycj-2023-0003. YANG S G, LUO Z, XU J H, et al. Failure modes of concrete structure under penetration and explosion [J]. Explosion and Shock Waves, 2024, 44(1): 015102. DOI: 10.11883/bzycj-2023-0003.
[22]	CHEN J S, WU C T, YOON S, et al. A stabilized conforming nodal integration for Galerkin mesh-free methods [J]. International Journal for Numerical Methods in Engineering, 2001, 50(2): 435–466. DOI: 10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A.
[23]	CHEN J S, WANG H P, YOON S, et al. Some recent improvements in meshfree methods for incompressible finite elasticity boundary value problems with contact [J]. Computational Mechanics, 2000, 25(2/3): 137–156. DOI: 10.1007/s004660050465.
[24]	尹华伟, 蒋轲, 张料, 等. 钢纤维混凝土板在冲击与爆炸荷载下的K&C模型 [J]. 高压物理学报, 2020, 34(3): 034205. DOI: 10.11858/gywlxb.20190853. YIN H W, JIANG K, ZHANG L, et al. K&C model of steel fiber reinforced concrete plate under impact and blast load [J]. Chinese Journal of High Pressure Physics, 2020, 34(3): 034205. DOI: 10.11858/gywlxb.20190853.
[25]	MAO L, BARNETT S, BEGG D, et al. Numerical simulation of ultra high performance fibre reinforced concrete panel subjected to blast loading [J]. International Journal of Impact Engineering, 2014, 64: 91–100. DOI: 10.1016/j.ijimpeng.2013.10.003.
[26]	CHEN L, XIE P C, FENG B, et al. A modified K&C model for concrete subjected to coupled effect of high temperature and high strain rate [J]. International Journal of Impact Engineering, 2023, 181: 104760. DOI: 10.1016/j.ijimpeng.2023.104760.
[27]	YANG S, LIANG Z Y, XU X Z, et al. A numerical simulation method for fragments distribution of concrete subjected to blast loading [J]. Engineering Failure Analysis, 2025, 176: 109606. DOI: 10.1016/j.engfailanal.2025.109606.
[28]	张传爱, 方秦, 陈力. 对DYNA3D中K&C混凝土模型的探讨 [J]. 工业建筑, 2010, 40(S1): 288–292. DOI: 10.13204/j.gyjz2010.s1.151. ZHANG C A, FANG Q, CHEN L. Discussion on K&C concrere model for concrte in DYNA3D [J]. Industrial Construction, 2010, 40(S1): 288–292. DOI: 10.13204/j.gyjz2010.s1.151.
[29]	胡金生, 杨秀敏, 王安宝, 等. 纤维混凝土抗接触爆炸性能研究 [C]//第十三届全国结构工程学术会议论文集. 吉安: 中国力学学会结构工程专业委员会, 南昌大学建筑工程学院, 中国力学学会《工程力学》编委会, 清华大学土木工程系, 2004: 56–59.
[30]	袁建虎, 唐建, 吕振坚, 等. 钢丝网高强混凝土抗爆性能试验研究 [J]. 兵工学报, 2012, 33(3): 373–378. YUAN J H, TANG J, LV Z J, et al. Experimental investigation on anti-explosion performance of steel-wire-net reinforced concretes [J]. Acta Armamentarii, 2012, 33(3): 373–378.
[31]	王德荣, 戴明, 李杰, 等. 钢纤维超高强活性混凝土(RPC)遮弹板接触爆炸破坏作用 [J]. 爆炸与冲击, 2008, 28(1): 68–75. DOI: 10.3321/j.issn:1001-1455.2008.01.012. WANG D R, DAI M, LI J, et al. Failure effect of steel-fiber reactive power concrete (RPC) shelter plate under contact explosion [J]. Explosion and Shock Waves, 2008, 28(1): 68–75. DOI: 10.3321/j.issn:1001-1455.2008.01.012.
[32]	焦楚杰. 高与超高性能钢纤维混凝土抗冲击和抗爆研究 [D]. 南京: 东南大学, 2005.
[33]	戎志丹, 孙伟, 张云升, 等. 超高性能钢纤维混凝土抗二次接触爆炸性能研究 [J]. 华北水利水电学院学报, 2012, 33(6): 1–4. DOI: 10.19760/j.ncwu.zk.2012.06.001. RONG Z D, SUN W, ZHANG Y S, et al. Study on the characteristics of ultra-high performance steel fiber reinforced concrete under the second explosion [J]. Journal of North China Institute of Water Conservancy and Hydroelectric Power, 2012, 33(6): 1–4. DOI: 10.19760/j.ncwu.zk.2012.06.001.