钙质砂场地爆炸成坑实验与数值模拟研究

黄杰; 李明鸿; 吴拓展; 宗周红

doi:10.11883/bzycj-2022-0556

钙质砂场地爆炸成坑实验与数值模拟研究

doi: 10.11883/bzycj-2022-0556

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: 国家重点研发计划（2021YFC3100700）

详细信息

作者简介:
黄　杰（1995－　），男，博士研究生，230208628@seu.edu.cn

通讯作者:
宗周红（1966－　），男，博士，教授， zongzh@seu.edu.cn

中图分类号: O383.1
计量
- 文章访问数: 473
- HTML全文浏览量: 106
- PDF下载量: 81
- 被引次数: 0
出版历程
- 收稿日期: 2022-12-13
- 修回日期: 2023-07-10
- 刊出日期: 2023-10-27

Experimental and numerical simulation studies on blast-induced craters in calcareous sand

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

摘要

摘要: 为了建立钙质砂场地爆炸成坑效应的计算方法，首先在开挖出的钙质砂模型场地开展了不同当量、不同埋深的野外爆炸实验，然后基于有限元与光滑粒子流耦合算法建立了适用于钙质砂爆炸成坑计算的数值模型，并分析了炸药形状和土体参数对爆坑形态的影响，最后建立了适用于钙质砂场地中的爆坑计算公式。结果表明：埋置爆下，钙质砂场地爆坑尺寸大于硅质砂土中的爆坑尺寸；光滑粒子流算法能较好地揭示钙质砂场地中爆坑轮廓的形成机理；炸药形状和土体密实度等参数对于钙质砂爆坑形态具有不同程度的影响，拟合得到的钙质砂场地接触爆和埋置爆抛掷型爆坑尺寸计算公式，可较好地预测不同爆炸当量作用下的爆炸成坑尺寸。
- 钙质砂场地 /
- 爆炸成坑 /
- 爆炸实验 /
- 光滑粒子流
Abstract: With the further development of ocean engineering, the dynamic response of calcareous sand sites under strong dynamic loading has received broad attention. In order to investigate the crater characteristics of calcareous sand sites under explosion impact, filed experiments and numerical simulations were conducted. Firstly, a series of field explosion experiments were conducted on calcareous sand sites, with different equivalent sizes and burial depths. The longitudinal and transverse diameter, as well as the depth of craters were measured for each case. Secondly, a new numerical algorithm (FEM-SPH) was used to simulate the formation process of explosion craters, combining the finite element model (FEM) and the smoothed particle hydrodynamics (SPH). Furthermore, the simulated crater dimensions were compared with the experimental results to validate the accuracy of the FEM-SPH model. Thanks to the advantage of the FEM-SPH in simulating large deformations, the crater formation process of ground contact explosions and buried explosions agreed well with the experimental results. The experiment research showed the crater size resulting from buried explosions is larger in calcareous sand compared to siliceous sand. The phenomenon was mainly attributed to the higher porosity and lower interparticle bonding strength of calcareous sand. With the validated FEM-SPH model, parametric analyses, including soil parameters and shapes of charges, were detailed discussed. Under the same equivalent, the influence of soil parameters on the size of the crater was about 6%, while the change in the shape of the charge caused a significant influence on the shape and size of the craters. Finally, empirical formulas were derived to determine the carter diameter and depth under cubic charge explosion according to the FEM-SPH numerical results in calcareous sand sites. The formulas can predict the dimensions of ground contact explosions and buried explosions within different equivalent charge weight ranges (0–500 kg). The above research results provided a useful reference for the blast-resistant protection design and emergency reinforcement of calcareous sand foundations.
- calcareous sand /
- blast crater /
- explosion experiment /
- smoothed particle hydrodynamics

HTML全文

区别于一般的爆炸力学和冲击动力学计算，毁伤仿真计算往往需要对完整目标场景甚至阵地场景进行武器打击全过程计算，同时又需要近实时给出计算结果。这种大场景和快速计算在武器研发和运用的工程实际中有着强烈的应用需求。现有爆炸和冲击动力学计算方法（如FEM）由于计算规模和计算效率的限制，在进行毁伤场景计算时往往只能对目标构件或者局部区域进行计算，很难满足毁伤仿真的应用需求。近年来出现了一些快速算法，如镜像爆源法、侵彻微分面元法和破片射线追踪法等，这些快速算法充分利用解析公式、经验数据或代理模型，结合计算机仿真与可视化技术，形成实用工具，有力支撑了国防工业和军事领域的应用。

毁伤快速算法的求解时间必须满足强制时间约束条件，在优先满足时间效率要求的前提下，综合采用解析公式、经验数据、数值计算、人工智能、计算机仿真等方法，进行算法创新和集成应用。毁伤快速算法是一种既区别于解析公式法，又区别于传统有限元的求解方法，既有解析公式稳健可靠的特性，又有有限元方法良好的复杂几何形状适用性，填补了解析公式和有限元方法之间巨大的方法空白。这类方法能够抓住毁伤的主要特征进行快速求解，其特点主要包括：复杂三维场景适用，时间差分推进，数据驱动为主、模型驱动为辅，“绝对的时效性、相对的准确性”，物理毁伤、功能毁伤和任务毁伤的一体化计算等。毁伤仿真是一个典型的多学科交叉、多技术融合的领域，尤其对于计算机图形学等计算机仿真学科和相关技术有很强的依赖性，典型例子就是射线追踪法（ray tracing）在破片场求解中的应用。此外，在实际应用中，对于软件友好操作、三维可视化等功能也有很强的技术需求，可以说毁伤快速算法和计算机仿真技术构成了深度耦合的关系。

根据工作需要，我国不少科研单位开展了一些相关基础研究，并形成了相应的研究成果，但是针对这一领域进行系统学术交流的平台一直缺乏。为了推动毁伤快速算法和仿真技术领域的科学发展，促进此类方法在国防安全领域的运用，2023年7月，在中国力学学会爆炸力学分会计算爆炸力学专业组的指导下，国防科技大学理学院和湖南大学土木工程学院联合承办了2023年毁伤快速算法与仿真技术研讨会，旨在探讨毁伤快速算法和仿真技术的关键技术和发展方向。我国本领域专家学者积极参会和投稿，贡献出了精彩的学术报告和高质量的学术论文，会议规模远超组委会的预期。经过《爆炸与冲击》期刊的严格审稿流程，多篇文章有幸获得发表，形成本期专题。会议组委会由衷感谢全部参会人员、论文作者和审稿专家，特别感谢《爆炸与冲击》编辑部为本专题出版做出的贡献！

国防科技大学卢芳云教授

图 1 钙质砂场地布设

Figure 1. Layout for calcareous sand site

下载: 全尺寸图片幻灯片

图 2 钙质砂试样

Figure 2. Calcareous sand sample

下载: 全尺寸图片幻灯片

图 3 地面接触爆炸工况和埋置爆炸工况的现场布置

Figure 3. Layouts of ground contact explosion and buried explosion sites

下载: 全尺寸图片幻灯片

图 4 地面接触爆的爆坑形态

Figure 4. Crater morphology induced by ground contact explosion

下载: 全尺寸图片幻灯片

图 5 爆坑的断面

Figure 5. Profile of an explosion-induced crater

下载: 全尺寸图片幻灯片

图 6 埋置爆形成的2类爆坑

Figure 6. Two types of craters induced by buried explosion

下载: 全尺寸图片幻灯片

图 7 爆坑比例直径随装药比例埋深的变化

Figure 7. Variation of scaled crater diameter with scaled charge burial depth

下载: 全尺寸图片幻灯片

图 8 FEM与SPH固连耦合方式

Figure 8. The attachment coupled approach between SPH and FEM

下载: 全尺寸图片幻灯片

图 9 1/4数值计算模型

Figure 9. 1/4 numerical model

下载: 全尺寸图片幻灯片

图 10 *MAT_005压力-变形曲线

Figure 10. Pressure-deformation curves for *MAT_005

下载: 全尺寸图片幻灯片

图 11 工况C2的横向爆坑最终轮廓

Figure 11. Final crater formations for case C2

下载: 全尺寸图片幻灯片

图 12 工况C6的横向爆坑最终轮廓

Figure 12. Final crater formations for case C6

下载: 全尺寸图片幻灯片

图 13 工况C2的爆坑速度流场

Figure 13. The velocity flow fields of the explosion-induced crater for case C2

下载: 全尺寸图片幻灯片

图 14 工况C6的爆坑速度流场

Figure 14. The velocity flow fields of the explosion-induced crater for case C6

下载: 全尺寸图片幻灯片

图 15 2种不同装药形状

Figure 15. Two different charge shapes

下载: 全尺寸图片幻灯片

图 16 不同装药形状的地面接触爆爆坑轮廓

Figure 16. Profiles of craters induced by ground contact explosions with different charge shapes

下载: 全尺寸图片幻灯片

图 17 不同装药形状的埋置爆爆坑轮廓

Figure 17. Profiles of craters induced by buried explosions with different charge shapes

下载: 全尺寸图片幻灯片

图 18 地面接触爆的爆坑尺寸与炸药当量的拟合曲线

Figure 18. Fitting curves between crater sizes and explosive equivalent for ground contact explosion

下载: 全尺寸图片幻灯片

图 19 埋置爆时D/(2d)随W^7/24/d的变化

Figure 19. Variation of D/(2d) with W^7/24/d for buried explosion

下载: 全尺寸图片幻灯片

表 1 实验工况

Table 1. Experimental cases

工况	W/kg	d/m	λ/(m∙kg^−1/3)	工况	W/kg	d/m	λ/(m∙kg^−1/3)
C1	0.2	0	−0.021	C6	0.4	0.5	0.712
C2	0.8	0	−0.026	C7	0.8	0.5	0.565
C3	1.6	0	−0.042	C8	0.2	1.0	1.731
C4	3.2	0	−0.033	C9	0.4	1.0	1.391
C5	0.2	0.5	0.876

下载: 导出CSV

表 2 地面接触爆的爆坑尺寸

Table 2. Sizes of craters induced by ground contact explosion

工况	W/kg	D₁/m	D₂/m	H/m
C1	0.2	0.64	0.65	0.23
C2	0.8	1.05	1.05	0.33
C3	1.6	1.10	1.08	0.28
C4	3.2	1.05	1.30	0.36

下载: 导出CSV

表 3 埋置爆的爆坑尺寸

Table 3. Sizes of craters induced by buried explosion

工况	W/kg	d/m	λ/(m∙kg^–1/3)	D₁/m	D₂/m	D_av/m	H/m	爆坑类型
C5	0.2	0.5	0.87	1.05	1.44	1.25	0.51	抛掷型
C6	0.4	0.5	0.71	1.32	1.50	1.41	0.70	抛掷型
C7	0.8	0.5	0.56	1.63		1.63	0.83	抛掷型
C8	0.2	1.0	1.73	1.00	0.95	0.98		塌陷型
C9	0.4	1.0	1.39	1.56	1.50	1.53		塌陷型

下载: 导出CSV

表 4 密实度为90%的钙质砂的材料参数

Table 4. Parameters of calcareous sand with the compactness of 90%

ε₁	ε₂	ε₃	ε₄	ε₅	ε₆	ε₇	ε₈	ε₉	ε₁₀
0	0.02	0.10	0.15	0.20	0.25	0.30	0.40	0.50	0.60

p₁/MPa	p₂/MPa	p₃/MPa	p₄/MPa	p₅/MPa	p₆/MPa	p₇/MPa	p₈/MPa	p₉/MPa	p₁₀/MPa
0	3.66	8.43	10.87	14.51	19.56	26.48	46.89	82.18	141.09

下载: 导出CSV

表 5 密实度为30%的钙质砂的材料参数^[19]

Table 5. Parameters of calcareous sand with the compactness of 30%^[19]

ε₁	ε₂	ε₃	ε₄	ε₅	ε₆	ε₇	ε₈	ε₉	ε₁₀
0	0.02	0.10	0.15	0.20	0.25	0.30	0.40	0.50	0.60

p₁/MPa	p₂/MPa	p₃/MPa	p₄/MPa	p₅/MPa	p₆/MPa	p₇/MPa	p₈/MPa	p₉/MPa	p₁₀/MPa
0	2.30	5.80	8.50	11.70	15.83	21.03	36.43	62.23	105.59

ρ_s/(g·cm⁻³)		G/MPa		K_u/MPa		a₀ /kPa²		a₁/kPa	a₂
1.780		107.7		647.3		84.77		16.23	0.777

下载: 导出CSV

表 6 爆坑尺寸的数值模拟结果与实测结果对比

Table 6. Comparison of simulated and measured results of sizes of explosion-induced craters

工况	W/kg	d/m	实测值/m			计算值/m			计算值与实测值的偏差/%
工况	W/kg	d/m	D₁	D₂	H	D₁	D₂	H	D₁	D₂	H
C1	0.2	0	0.64	0.65	0.23	0.49	0.69	0.25	–23.4	6.20	8.70
C2	0.8	0	1.05	1.05	0.33	0.86	0.89	0.42	–18.9	–15.20	27.20
C3	1.6	0	1.10	1.08	0.28	1.09	1.13	0.38	–0.9	4.60	35.70
C5	0.2	0.5	1.05	1.44	0.51	1.04	1.10	0.73	–0.9	–23.60	43.10
C6	0.4	0.5	1.32	1.50	0.70	1.19	1.31	0.76	–9.8	–12.67	8.60
C7	0.8	0.5	1.63		0.83	1.63	1.63	0.80	0.6		–3.61

下载: 导出CSV

表 7 不同装药形状下爆坑尺寸对比

Table 7. Comparison of sizes of craters induced by explosions with different charge shapes

W/kg	d/m	长方体装药			立方体装药
W/kg	d/m	D₁	D₂	H/m	D/m	H/m
0.4	0	0.68	1.18	0.16	0.83	0.28
0.4	0.5	1.19	1.31	0.76	1.39	0.78

下载: 导出CSV

表 8 不同密实度钙质砂的爆坑尺寸对比

Table 8. Comparison of sizes of craters induced by explosions in calcareous sand with different compactness

密实度/%	W/kg	d/m	D/m	H/m	直径变化/%	深度变化/%
30	0.2	0	0.77	0.25	5.2	4.0
90	0.2	0	0.73	0.24	5.2	4.0
30	0.8	0	0.99	0.32	1.0	6.3
90	0.8	0	0.98	0.30	1.0	6.3
30	0.4	0.5	1.34	0.79	−3.6	2.6
90	0.4	0.5	1.39	0.78	−3.6	2.6
30	0.8	0.5	1.70	0.83	−3.4	1.2
90	0.8	0.5	1.76	0.82	−3.4	1.2

下载: 导出CSV

表 9 立方体装药地面接触爆形成的爆坑的尺寸的计算结果

Table 9. Numerical results of sizes of craters induced by ground contact explosions using cubic TNT charges

工况	W/kg	d/m	D/m	H/m	工况	W/kg	d/m	D/m	H/m
E1	0.20	0	0.73	0.24	E7	9.50	0	1.69	0.55
E2	0.40	0	0.83	0.28	E8	20.00	0	2.11	0.71
E3	0.80	0	0.98	0.30	E9	35.00	0	2.21	0.92
E4	1.63	0	1.19	0.35	E10	53.00	0	2.62	1.06
E5	2.80	0	1.21	0.39	E11	89.00	0	2.73	1.08
E6	6.67	0	1.52	0.49	E12	100.00	0	3.06	1.09

下载: 导出CSV

表 10 立方体装药埋置爆形成的爆坑的尺寸的计算结果

Table 10. Numerical results of sizes of craters induced by buried explosions using cubic TNT charges

工况	W/kg	d/m	D/m	工况	W/kg	d/m	D/m
D1	0.80	0.5	1.76	D8	200.00	1.5	8.30
D2	0.40	0.5	1.39	D9	200.00	2.0	7.49
D3	1.20	0.5	2.02	D10	286.00	1.5	8.89
D4	0.83	0.8	1.72	D11	350.00	2.0	8.90
D5	0.40	0.8	1.51	D12	420.00	2.0	9.80
D6	100.00	1.2	7.04	D13	512.00	1.5	10.81
D7	150.00	1.5	7.14	D14	512.00	2.5	10.60

下载: 导出CSV

参考文献(21)

[1]	YU X, CHEN L, FANG Q, et al. Determination of attenuation effects of coral sand on the propagation of impact-induced stress wave [J]. International Journal of Impact Engineering, 2019, 125: 63–82. DOI: 10.1016/j.ijimpeng.2018.11.004.
[2]	OUYANG H R, DAI G L, QIN W, et al. Dynamic behaviors of calcareous sand under repeated one-dimensional impacts [J]. Soil Dynamics and Earthquake Engineering, 2021, 150: 106891. DOI: 10.1016/j.soildyn.2021.106891.
[3]	DONG K, REN H Q, RUAN W J, et al. Dynamic mechanical behavior of different coral sand subjected to impact loading [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2021, 235(9): 1512–1523. DOI: 10.1177/0954406220967683.
[4]	KINNEY G F, GRAHAM K J. Explosive shocks in air [M]. Berlin: Springer, 1985.
[5]	贾永胜, 王维国, 谢先启, 等. 低含水率砂土和饱和砂土场地爆炸成坑特性实验 [J]. 爆炸与冲击, 2017, 37(5): 799–806. DOI: 10.11883/1001-1455(2017)05-0799-08. JIA Y S, WANG W G, XIE X Q, et al. Characterization of blast-induced craters in low-moisture and saturated sand from field experiments [J]. Explosion and Shock Waves, 2017, 37(5): 799–806. DOI: 10.11883/1001-1455(2017)05-0799-08.
[6]	XU R Z, CHEN L, ZHENG Y Z, et al. Study of crater in the Gobi desert induced by ground explosion of large amounts of TNT explosive up to 10 tons [J]. Shock and Vibration, 2021, 2021: 7357877. DOI: 10.1155/2021/7357877.
[7]	LUCCIONI B, AMBROSINI D, NURICK G, et al. Craters produced by underground explosions [J]. Computers & Structures, 2009, 87(21/22): 1366–1373. DOI: 10.1016/j.compstruc.2009.06.002.
[8]	DE A. Numerical simulation of surface explosions over dry, cohesionless soil [J]. Computers and Geotechnics, 2012, 43: 72–79. DOI: 10.1016/j.compgeo.2012.02.007.
[9]	穆朝民, 任辉启, 辛凯, 等. 变埋深条件下土中爆炸成坑效应 [J]. 解放军理工大学学报(自然科学版), 2010, 11(2): 112–116. DOI: 10.3969/j.issn.1009-3443.2010.02.003. MU C M, REN H Q, XIN K, et al. Effects of crater formed by explosion in soils [J]. Journal of PLA University of Science and Technology (Natural Science Edition), 2010, 11(2): 112–116. DOI: 10.3969/j.issn.1009-3443.2010.02.003.
[10]	ZHAO X H, WANG G H, LU W B, et al. Damage features of RC slabs subjected to air and underwater contact explosions [J]. Ocean Engineering, 2018, 147: 531–545. DOI: 10.1016/j.oceaneng.2017.11.007.
[11]	钟诗蕴, 孙鹏楠, 吕鸿冠, 等. SPH理论和方法在高速水动力学中的研究进展 [J]. 中国舰船研究, 2022, 17(3): 29–48. DOI: 10.19693/j.issn.1673-3185.02758. ZHONG S Y, SUN P N, LV H G, et al. Research progress of smoothed particle hydrodynamics and its applications in high-speed hydrodynamic problems [J]. Chinese Journal of Ship Research, 2022, 17(3): 29–48. DOI: 10.19693/j.issn.1673-3185.02758.
[12]	王维国, 刘汉龙, 陈育民, 等. 砂土地基触地爆炸的SPH-FEM耦合分析方法 [J]. 解放军理工大学学报(自然科学版), 2013, 14(3): 271–276. DOI: 10.3969/j.issn.1009-3443.2012.06.210. WANG W G, LIU H L, CHEN Y M, et al. Coupled SPH-FEM method for analyzing touchdown explosion in sand foundation [J]. Journal of PLA University of Science and Technology (Natural Science Edition), 2013, 14(3): 271–276. DOI: 10.3969/j.issn.1009-3443.2012.06.210.
[13]	王志亮, 毕程程, 李鸿儒. 混凝土爆破损伤的SPH-FEM耦合法数值模拟 [J]. 爆炸与冲击, 2018, 38(6): 1419–1428. DOI: 10.11883/bzycj-2017-0209. WANG Z L, BI C C, LI H R. Numerical simulation of blasting damage in concrete using a coupled SPH-FEM algorithm [J]. Explosion and Shock Waves, 2018, 38(6): 1419–1428. DOI: 10.11883/bzycj-2017-0209.
[14]	YANG G D, WANG G H, LU W B, et al. A SPH-Lagrangian-Eulerian approach for the simulation of concrete gravity dams under combined effects of penetration and explosion [J]. KSCE Journal of Civil Engineering, 2018, 22(8): 3085–3101. DOI: 10.1007/s12205-017-0610-1.
[15]	中国住房和城乡建设部. 土工试验方法标准: GB/T 50123—2019 [S]. 北京: 中国计划出版社, 2019.
[16]	US Department of the Army. Fundamentals of protective design for conventional weapons: TM5-855-1 [S]. Washington, USA: US Department of the Army, 1986.
[17]	王维国, 陈育民, 杨贵, 等. 湿砂场地爆炸成坑效应的现场试验与数值模拟研究 [J]. 岩石力学与工程学报, 2016, 35(1): 68–75. DOI: 10.13722/j.cnki.jrme.2015.0171. WANG W G, CHEN Y M, YANG G, et al. Field tests and numerical simulations of blast-induced crater in wet sands [J]. Chinese Journal of Rock Mechanics and Engineering, 2016, 35(1): 68–75. DOI: 10.13722/j.cnki.jrme.2015.0171.
[18]	谢述春, 姜春兰, 王在成, 等. 多层混凝土介质内爆炸相似性分析 [J]. 兵工学报, 2019, 40(6): 1198–1206. DOI: 10.3969/j.issn.1000-1093.2019.06.010. XIE S C, JIANG C L, WANG Z C, et al. Analysis of similarity law of explosion in multi-layer concrete medium [J]. Acta Armamentarii, 2019, 40(6): 1198–1206. DOI: 10.3969/j.issn.1000-1093.2019.06.010.
[19]	吴拓展, 宗周红, 李明鸿, 等. 浅埋单药包爆炸作用下饱和钙质砂基础液化数值模拟 [J]. 东南大学学报(自然科学版), 2022, 52(2): 237–246. DOI: 10.3969/j.issn.1001-0505.2022.02.005. WU T Z, ZONG Z H, LI M H, et al. Numerical simulation of liquefaction in saturated calcareous sand foundation induced by single charge shallow-buried explosion [J]. Journal of Southeast University (Natural Science Edition), 2022, 52(2): 237–246. DOI: 10.3969/j.issn.1001-0505.2022.02.005.
[20]	董凯. 爆炸冲击下珊瑚砂动态力学特性研究 [D]. 南京: 南京理工大学, 2021. DONG K. Dynamic mechanical behavior of coral sand subjected to blast and impact loading [D]. Nanjing, Jiangsu, China: Nanjing University of Science and Technology , 2021.
[21]	郝保田. 地下核爆炸及其应用 [M]. 北京: 国防工业出版社, 2002.