典型战斗部侵彻爆炸下块石混凝土的遮弹层设计

吴昊; 张瑜; 程月华; 岑国华

doi:10.11883/bzycj-2024-0136

典型战斗部侵彻爆炸下块石混凝土的遮弹层设计

doi: 10.11883/bzycj-2024-0136

同济大学土木工程学院，上海 200092

基金项目: 国家自然科学基金（52308522）；工程材料与结构冲击振动四川省重点实验室开放基金（23kfgk01）

详细信息

作者简介:
吴　昊（1981－　），男，博士，教授，wuhaocivil@tongji.edu.cn

通讯作者:
程月华（1994－　），女，博士，讲师，yhcheng@tongji.edu.cn

中图分类号: O385
计量
- 文章访问数: 194
- HTML全文浏览量: 14
- PDF下载量: 93
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-15
- 修回日期: 2024-09-19
- 网络出版日期: 2024-09-23

Design of rock-rubble concrete shield against the combination of penetration and explosion of warheads

College of Civil Engineering, Tongji University, Shanghai 200092, China

摘要

摘要: 针对钻地武器战斗部侵彻爆炸作用下块石混凝土遮弹层的抗力评估与工程设计，首先，提出了块石混凝土遮弹层的有限元建模方法，其可靠性通过含不同粗骨料类型（刚玉和玄武岩）、粒径（5~15 mm、5~20 mm、35~45 mm和65~75 mm）和体积率（15%和30%）的超高性能混凝土靶体的准静态和弹体侵彻试验进行验证。然后，以小直径炸弹SDB侵彻半无限厚块石混凝土靶体为基准工况，定量分析了块石类型（刚玉、玄武岩和花岗岩）和无量纲块石粒径（0.3~2.2倍弹径）对侵彻深度的影响，并确定了最优设计原则。最后，开展了3种典型钻地武器（SDB、WDU-43/B和BLU-109/B）的侵彻效应分析，定量对比了普通强度混凝土（normal strength concrete, NSC）、超高性能混凝土（ultra-high performance concrete, UHPC）和刚玉块石混凝土（corundum rubble concrete, CRC）的抗侵彻能力，提出了原型战斗部侵彻爆炸作用下刚玉块石混凝土遮弹层的工程设计方法。结果表明：粒径为1.3~1.7倍弹径的CRC遮弹层抗侵彻性能最优；3种战斗部侵彻作用下最优设计CRC遮弹层的侵彻深度分别为0.29、0.78和0.68 m，较NSC和UHPC遮弹层分别降低了61.8%~69.1%和43.3%~58.0%；3种战斗部侵彻爆炸作用下CRC遮弹层的临界贯穿及震塌厚度分别为0.55、1.41和1.48 m及1.11、2.26和3.17 m，与NSC和UHPC遮弹层相比，临界贯穿厚度分别降低了58.5%~61.2%和43.2%~58.1%，临界震塌厚度分别降低了61.8%~69.2%和34.7%~40.5%。
- 块石混凝土遮弹层 /
- 侵彻爆炸 /
- 临界贯穿 /
- 临界震塌 /
- 防护设计
Abstract: Aiming at the resistance evaluation and engineering design of the rock-rubble concrete shield under the combination of penetration and explosion of Earth Penetrating Weapons, firstly, a finite element modeling method for rock-rubble concrete shields was proposed. By conducting numerical simulations of quasi-static and penetration tests on ultra-high performance concrete targets containing different coarse aggregate types (corundum and basalt), particle sizes (5–15 mm, 5–20 mm, 35–45 mm, and 65–75 mm), and volume fractions (15% and 30%), the reliability of the finite element analysis approach was thoroughly verified. Then, using the semi-infinite rock-rubble concrete shield penetrated by the SDB as a case study, the quantitative influence of type (corundum, basalt, and granite) and dimensionless particle size of rock-rubble (ranging from 0.3 to 2.2 times the projectile diameter) on the penetration depth was analyzed, and optimal design recommendations were determined. Furthermore, the penetration analyses of three typical prototype warheads, i.e., SDB, WDU-43/B, and BLU-109/B, were carried out, and the corresponding penetration resistances of normal strength concrete (NSC), ultra-high performance concrete (UHPC), and corundum rubble concrete (CRC) shields against the above three warheads were quantitatively compared. Finally, the engineering design method for the CRC shield under the combined effects of penetration and explosion of prototype warheads was proposed. The results indicate that the CRC shield containing the particle size of 1.3 to 1.7 times the projectile diameter exhibits the most excellent penetration resistance. Under the penetration of three types of warheads, the penetration depths in CRC shield were 0.29, 0.78, and 0.68 m, respectively, which are reduced by 61.8%–69.1% and 43.3%–58.0% compared to those in NSC and UHPC shields. Under the combined effects of penetration and explosion, the perforation limits of the CRC shield are 0.55, 1.41, and 1.48 m, while the scabbing limits are 1.11, 2.26, and 3.17 m. Compared with NSC and UHPC shields, the perforation limits are reduced by 58.5%–61.2% and 43.2%–58.1%, respectively, and the scabbing limits are reduced by 61.8%–69.2% and 34.7%–40.5%, respectively.
- rock-rubble concrete shield /
- penetration and explosion /
- perforation limit /
- scabbing limit /
- protective design

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图 1 战斗部几何尺寸（单位：mm）

Figure 1. Geometric dimensions of warheads (Unit: mm)

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图 2 块石混凝土遮弹层建模

Figure 2. Modelling of rock-rubble concrete shield

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图 3 有限元模型及数值模拟结果

Figure 3. Finite element model and numerical simulation results

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图 4 有限元模型和数值模拟结果

Figure 4. Finite element model and numerical simulation results

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图 5 含刚玉骨料UHPC靶体有效塑性应变云图

Figure 5. Effective plastic strain contours of corundum aggregated UHPC targets

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图 6 原型战斗部侵彻块石混凝土遮弹层数值仿真策略

Figure 6. Numerical simulation strategy for prototype warheads penetrating on rock-rubble concrete shields

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图 7 3种类型块石混凝土遮弹层侵彻深度（单位：mm）

Figure 7. Penetration depths of three types rock-rubble concrete shields (Unit: mm)

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图 8 弹体变形和破坏形态

Figure 8. Deformation and fracture patterns of projectiles

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图 9 4种粒径CRC遮弹层侵彻深度（单位：mm）

Figure 9. Penetration depths of CRC shields with four particle sizes (Unit: mm)

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图 10 3种战斗部侵彻CRC遮弹层侵彻深度（单位：mm）

Figure 10. Penetration depths of CRC shields with three warheads (Unit: mm)

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图 11 CRC与NSC和UHPC遮弹层的对比

Figure 11. Comparisons of CRC with NSC and UHPC shields

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表 1 弹体JC模型参数^[23-24]

Table 1. JC model parameters of projectile ^[23-24]

ρ/(kg·m^–3)	G/GPa	A/MPa	B/MPa	N	C	M	T_m/K	T_r/K	c_V/(J·kg^–1·K^–1)	${\dot \varepsilon _0}$
7 800	81	792	2 483	0.474	0.009	1.07	1 793	298	477	1.0×10^–4

D₁	D₂	D₃	D₄	D₅	C/(m·s^–1)	S₁	S₂	S₃	γ₀	α
0.692	1.581	–3.053	–0.042	2.98	4 569	1.49	0	0	2.17	0.46

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表 2 刚玉JH-2模型参数^[27-28]

Table 2. JH-2 model parameters of corundum^[27-28]

ρ/(kg·m^–3)	G/GPa	A₀	B₀	N₀	C	M₀
3 800	152	0.88	0.431	0.64	0.007	0.6

${\dot \varepsilon _0}$	T/GPa	σ_HEL/GPa	p_HEL/GPa	D₁₀	D₂₀	F_s
1.0	2.62	6.75	3.65	0.012 5	1.85	1.5

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表 3 玄武岩、花岗岩和UHPC基体HJC模型参数^[29-30]

Table 3. HJC model parameters of basalt, granite and UHPC matrix ^[29-30]

组分	ρ/(kg·m^–3)	G/GPa	A₁/MPa	B₁/MPa	N₁	C	f_c^'/MPa	T_max/MPa	${\dot \varepsilon _0}$	ε_min
玄武岩	3 000	32.25	0.3	1.73	0.79	0.005	120	6.792	1.0	0.01
花岗岩	2 660	30.50	0.3	1.73	0.79	0.005	154	7.694	1.0	0.01
基体	2 500	24.02	0.3	1.73	0.79	0.005	115	6.649	1.0	0.01

组分	S_max	p_c/MPa	μ_c/10⁻⁵	p_l/GPa	μ_l	D₁₁	D₂₁	K₁/GPa	K₂/GPa	K₃/GPa
玄武岩	7.0	40	93	3.47	0.1	0.04	1.0	116	–243	506
花岗岩	7.0	51	126	3.47	0.11	0.04	1.0	116	–243	506
基体	7.0	38.33	119.7	3.47	0.08	0.04	1.0	116	–243	506

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表 4 块石和UHPC基体界面参数

Table 4. Parameters of interface between rock-rubble and UHPC matrix

法向强度/MPa	法向断裂能/(MN·mm^–1)	切向强度/MPa	切向断裂能/(MN·mm^–1)	法向刚度/(GPa·m^–1)	切/法向刚度比	损伤指数
9	1	27	3	5	0.42	–2

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表 5 立方体单轴压缩试验结果

Table 5. Cube uniaxial compression test results

工况	骨料类型	粒径/mm	体积率%	抗压强度/MPa		误差%
工况	骨料类型	粒径/mm	体积率%	试验值	模拟值	误差%
5-20BA15%	玄武岩	5～20	15	115.5	115.3 (114/115/117)	−0.1
5-20BA30%	玄武岩	5～20	30	118.9	121.7 (121/121/123)	2.3
5-20CA15%	刚玉	5～20	15	123.0	121.0 (116/127/120)	−1.6
5-20CA30%	刚玉	5～20	30	137.1	138.0 (137/139/138)	0.7
35-45CA30%	刚玉	35～45	30	145.3	148.7 (142/154/150)	2.3

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表 6 试验工况及侵彻深度结果

Table 6. Test cases and penetration depths

工况	骨料类型	粒径/mm	体积率/%	侵彻深度/mm		误差/%
工况	骨料类型	粒径/mm	体积率/%	试验值^[8-9]	模拟值	误差/%
5-20CA30%	刚玉	5～20	30	99.5(98/101)	101.1(92.3/109.5/94.2/113.3/96.2)	1.6
35-45CA30%	刚玉	35～45	30	44.5(21/68)	51.6(45.3/53.3/46.9/56.8/55.8)	16.0
65-75CA30%	刚玉	65～75	30	48.0(59/37)	50.9(56.2/47.8/45.4/50.8/54.2)	6.0
5-15BA30%	玄武岩	5～15	30	122.0(124/120)	124.8(124.9/126.4/126.5/123.0/123.2)	2.3

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表 7 网格尺寸过渡计算结果的对比

Table 7. Comparisons of results for various mesh sizes

块石类型	模型	侵彻深度/mm		误差/%	弹体残余长度/mm		误差/%
块石类型	模型	2 mm+2 mm	5 mm+10 mm	误差/%	2 mm+2 mm	5 mm+10 mm	误差/%
刚玉	1	108.0	107.3	0.65	320.8	316.1	1.47
	2	95.1	93.9	1.26	315.4	311.4	1.27
	3	103.7	102.2	1.45	317.5	312.6	1.54
	平均值	102.3	101.1	1.17	317.9	313.4	1.43
玄武岩	1	132.1	130.5	1.21	327.8	334.8	−2.14
	2	117.3	115.7	1.36	320.2	325.9	−1.78
	3	128.3	125.8	1.95	324.6	330.3	−1.76
	平均值	125.9	124.0	1.51	324.2	330.3	−1.89
花岗岩	1	134.0	134.3	−0.22	333.2	331.0	0.66
	2	119.5	118.9	0.50	342.3	345.7	−0.99
	3	130.4	127.9	1.92	337.4	342.6	−1.55
	平均值	128.0	127.0	0.78	337.6	339.8	−0.63

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表 8 不同遮弹层模拟结果

Table 8. Simulation results of different shields

工况	块石类型	无量纲粒径范围	块石体积率/%	侵彻深度/mm	弹体残余长度/mm
0.8-1.2CA43%	刚玉	0.8D～1.2D	43.1	361.5	1 480
0.8-1.2BA43%	玄武岩	0.8D～1.2D	43.1	588.1	1 620
0.8-1.2GA43%	花岗岩	0.8D～1.2D	43.1	617.2	1 630
0.3-0.7CA46%	刚玉	0.3D～0.7D	46.6	664.9	1 585
0.8-1.2CA42%	刚玉	0.8D～1.2D	42.4	369.8	1 505
1.3-1.7CA41%	刚玉	1.3D～1.7D	41.9	289.7	1 415
1.8-2.2CA40%	刚玉	1.8D～2.2D	40.3	275.7	1 300

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表 9 3种战斗部的数值模拟结果

Table 9. Numerical simulation results with three warheads

战斗部	侵彻深度/m			临界贯穿系数^[18-19]	临界贯穿厚度/m			临界震塌系数^[18-19]	临界震塌厚度/m
战斗部	CRC	UHPC^[19]	NSC^[18]	临界贯穿系数^[18-19]	CRC	UHPC^[19]	NSC^[18]	临界震塌系数^[18-19]	CRC	UHPC^[19]	NSC^[18]
SDB	0.29	0.69	0.94	1.88	0.55	1.30	1.40	3.83	1.11	1.70	3.60
WDU-43/B	0.78	1.41	2.17	1.81	1.41	2.55	3.40	2.90	2.26	3.80	6.30
BLU-109/B	0.68	1.20	1.78	2.17	1.48	2.60	3.80	4.66	3.17	5.00	8.30

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