运用极限荷载法研究钢筋混凝土板低速侵彻效应

王德荣; 苏杭; 程怡豪; 冯淑芳

doi:10.11883/1001-1455(2017)05-0837-07

运用极限荷载法研究钢筋混凝土板低速侵彻效应

doi: 10.11883/1001-1455(2017)05-0837-07

1.
中国人民解放军陆军工程大学爆炸冲击防灾减灾国家重点实验室，江苏南京 210007
2.
北部战区陆军第二工程科研设计所，辽宁沈阳 110162

基金项目:

国家自然科学基金项目 51409258

长江学者与创新团队发展计划项目 IRT13071

详细信息

作者简介:
王德荣(1968—)，男，博士，副教授, wdrjb@163.com

中图分类号: O347
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- 被引次数: 1
出版历程
- 收稿日期: 2016-01-11
- 修回日期: 2016-08-08
- 刊出日期: 2017-09-25

Response of reinforced concrete slabs to low-velocity projectile impact investigated using upper bound method

1.
State Key Laboratory of Disaster Prevention and Mitigation of Explosive and Impact, The Army Engineering University of PLA, Nanjing 210007, Jiangsu, China
2.
The Second Institute of Engineering Research and Design, Northern Theater Army, Shenyang 110162, Liaoning, China

摘要

摘要: 基于不可压缩刚塑性材料模型和滑移线场理论，获得了单一容许速度场条件下刚性弹低速侵彻半无限介质的阻力函数。在此基础上，基于多速度容许场得到了刚性弹侵彻有限厚度靶的三阶段阻力曲线，并提出了震塌与贯穿的临界条件，通过与实验结果、UMIST公式及古比雪夫的对比，验证了本文方法在钢筋混凝土板低速撞击问题中的适用性,分析了弹头形状、冲击因子和钢筋阻力系数等参数对临界震塌(贯穿)厚度的影响。
- 刚塑性极限分析 /
- 低速侵彻 /
- 混凝土 /
- 震塌 /
- 贯穿
Abstract: Based on the incompressible-rigid-plastic material assumption and the slip line field theory, the resistance function of a rigid projectile penetrating a semi-infinite target at a low velocity was obtained with a single admissible velocity field. A three-stage resistance curve of a rigid projectile impacting on a thin target was analyzed under multiple velocity fields, where the critical conditions for scabbing or perforation were calculated. The methods and formulae for local effects on reinforced concrete slab under low-velocity impact were further verified using comparative analysis of the results from the experiments, the UMIST formulae, the Kuibyshev formulae, and the present paper's calculations. The relationships between the normalized critical scabbing/perforation thickness, and the nose-shape factor, the impact factor and the reinforcement factor were examined to present potential guide to experimental studies.
- rigid-plasticity limit analysis /
- low velocity penetration /
- concrete /
- scabbing /
- perforation

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图 1 锥形头弹侵彻半无限靶的容许速度场

Figure 1. Admissible velocity field of semi-infinite target under penetration of cone-nosed projectile

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图 2 平头弹条件下阻力上限

Figure 2. Upper bound of penetration resistance for flat-nosed projectile

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图 3 不同条件下侵彻阻力上限曲线

Figure 3. Upper bound of penetration resistance curves under different conditions

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图 4 本文公式与UMIST公式、古比雪夫公式的比较

Figure 4. Comparison between UMIST formulae, Kuibyshev formulae and this paper's formule

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图 5 临界震塌和贯穿厚度随冲击因子与钢筋阻力系数的变化

Figure 5. Normalized critical scabbing or perforation thickness versus impact factor and reinforcement factor

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表 1 本文计算结果与实验^[10]的比较

Table 1. Comparison between experimental results^[10] and present method

实验	L/2a	f_c /MPa	f_t/MPa	τ_s/MPa	I_BL	v_BL/(m·s^-1)
实验	L/2a	f_c /MPa	f_t/MPa	τ_s/MPa	I_BL	实验	本文计算
T-1	2	25.0	2.6	4.0	10.5	27.0~35.7	47
T-2	2	25.2	3.1	4.4	10.5	41.7~56.8	49
T-3	2	161.9	7.3	17.2	10.5	34.7~58.5	97
T-4	2	175.3	13.8	24.6	10.5	76.0~104.0	116

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表 2 本文计算结果与普通混凝土实验^[11]的比较

Table 2. Comparison between experimental results ^[11] of normal strength concrete and present method

实验	L/2a	f_c /MPa	f_t/MPa	τ_s/MPa	I_BL	φ/mm	@/mm	f_s/MPa	μ	v_BL/(m·s^-1)
实验	L/2a	f_c /MPa	f_t/MPa	τ_s/MPa	I_BL	配筋		f_s/MPa	μ	实验	本文计算
D-1-1	2.0	35.0	3.0	5.12	15.9	2.5	34	382	0.43	165	103
D-1-2	2.0	35.0	3.0	5.12	15.4	3.0	25	183	0.40	222	101
D-1-3	2.4	35.0	3.0	5.12	20.8	3.0	25	183	0.40	232	117
D-1-4	2.4	35.0	3.0	5.12	127.1	5.0	27	473	2.68	236	291
D-1-5	2.0	34.0	3.4	5.38	53.6	3.25	21	600	1.76	210	193
D-1-6	2.0	34.0	3.4	5.38	34.8	2.5	20	650	1.19	162	156

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表 3 本文计算结果与高性能混凝土实验^[12]的比较

Table 3. Comparison between experimental results^[12] of high performance concrete and present method

实验	L/2a	f_c /MPa	f_t/MPa	τ_s/MPa	I_BL	φ/mm	@/mm	f_s/MPa	μ	v_BL/(m·s^-1)
实验	L/2a	f_c /MPa	f_t/MPa	τ_s/MPa	I_BL	配筋		f_s/MPa	μ	实验	本文计算
D-2-1	4	40.0	4.0	6.3	66.5	8	100	400	0.64	204~245	187
D-2-2	4	108.0	10.8	17.1	38.3	8	100	400	0.24	273~276	233
D-2-3	4	102.0	10.2	16.1	39.1	8	100	400	0.25	281~289	229
D-2-4	4	104.0	10.4	16.4	38.9	8	100	400	0.24	287~291	231
D-2-5	4	113.0	11.3	17.9	37.7	8	100	400	0.22	262~289	237
D-2-6	4	106.0	10.6	16.8	38.6	8	100	400	0.24	291~307	232
D-2-7	4	101.0	10.1	16.0	39.3	8	100	400	0.25	286~292	229
D-2-8	4	93.0	9.3	14.7	40.7	8	100	400	0.27	292~313	223
D-2-9	4	94.0	9.4	14.9	40.5	8	100	400	0.27	313~314	224
D-2-10	4	102.0	10.2	16.1	39.2	8	100	400	0.25	287~289	229
D-2-11	4	103.0	10.3	16.3	39.0	8	100	400	0.25	287~292	230

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参考文献(16)

[1]	Hill R. The mathematical theory of plasticity[M]. Oxford: Clarendon Press, 1950.
[2]	Ravid M, Bodner S R. Dynamic perforation of visco-plastic plates by rigid projectiles[J]. International Journal of Engineering Science, 1983, 21(6):577-591. doi: 10.1016/0020-7225(83)90105-2
[3]	Amini A, Anderson J. Modeling of projectile penetration into geologic targets based on energy tracking and momentum impulse principles[C]//Proceedings of the Sixth International Symposium on Interaction of Nonnuclear Munitions with Structures. Germany, 1993.
[4]	Tirosh J, Tylis A, Davidi G. Foreign object damage: Penetration of rigid projectiles into solids[J]. Mechanics of Materials, 2009, 41(5):535-544. doi: 10.1016/j.mechmat.2009.01.024
[5]	陈士林, 王明洋, 潘越峰.锥形端部弹体在岩石(混凝土)介质层中侵彻实用计算方法[J].爆炸与冲击, 2004, 24(1):7-15. http://www.bzycj.cn/article/id/9912 Chen Shilin, Wang Mingyang, Pan Yuefeng. The method of calculation for penetration of conical nosed projectile in rock (concrete) layers[J]. Explosion and Shock Waves, 2004, 24(1):7-15. http://www.bzycj.cn/article/id/9912
[6]	王明洋, 施翠英, 陈士林.事故型撞击混凝土板的临界震塌与贯穿厚度计算方法[J].工程力学, 2009, 26(11):238-246. http://www.cnki.com.cn/Article/CJFDTotal-GCLX200911042.htm Wang Mingyang, Shi Cuiying, Chen Shilin. Method of calculating critical spalling and penetration thickness of concrete slab of block under accident impact[J]. Engineering Mechanics, 2009, 26(11):238-246. http://www.cnki.com.cn/Article/CJFDTotal-GCLX200911042.htm
[7]	冯淑芳, 王明洋, 任广昊, 等.深地下坑道衬砌结构抗局部冲击计算方法研究[J].岩石力学与工程学报, 2011, 30(6):1150-1156. http://d.old.wanfangdata.com.cn/Periodical/yslxygcxb201106008 Feng Shufang, Wang Mingyang, Ren Guanghao, et al. Research on calculation method for local impact of deep tunnel lining structure[J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(6):1150-1156. http://d.old.wanfangdata.com.cn/Periodical/yslxygcxb201106008
[8]	咸玉席, 文鹤鸣.平头弹侵彻半无限混凝土靶的工程模型[J].防护工程, 2012, 34(2):35-38. http://cdmd.cnki.com.cn/Article/CDMD-10358-1014432193.htm Xian Yuxi, Wen Heming. An engineering model for the penetration of flat-nosed projectiles into semi-infinite concrete targets[J]. Protective Engineering, 2012, 34(2):35-38. http://cdmd.cnki.com.cn/Article/CDMD-10358-1014432193.htm
[9]	Li Q M, Ye Z Q, Ma G W, et al. Influence of overall structural response on perforation of concrete targets[J]. International Journal of Impact Engineering, 2007, 34(5):926-941. doi: 10.1016/j.ijimpeng.2006.03.005
[10]	Tai Y S. Flat ended projectile penetrating ultra-high strength concrete plate target[J]. Theoretical and Applied Fracture Mechanics, 2009, 51(2):117-128. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ0214989790/
[11]	Dancygier A N. Effect of reinforcement ratio on the resistance of reinforced concrete to hard projectile impact[J]. Nuclear Engineering and Design, 1997, 172(1):233-245. http://cn.bing.com/academic/profile?id=723b6881b18fa7ba33bf200ca91ae81f&encoded=0&v=paper_preview&mkt=zh-cn
[12]	Dancygier A N, Yankelevsky D Z, Jaegermann C. Response of high performance concrete plates to impact of non-deforming projectiles[J]. International Journal of Impact Engineering, 2007, 34(11):1768-1779. doi: 10.1016/j.ijimpeng.2006.09.094
[13]	卡恰诺夫L M.塑性理论基础(第二版)[M].周承倜, 译.北京: 人民教育出版社, 1982: 332-385.
[14]	冯淑芳.深埋地下结构抗爆动力计算方法研究[D].南京: 解放军理工大学, 2011.
[15]	徐秉业, 刘信声.应用弹塑性力学[M].北京:清华大学出版社, 1995:510-512.
[16]	Wen H M, Xian Y U. A unified approach for concrete impact[J]. International Journal of Impact Engineering, 2015, 77:84-96. doi: 10.1016/j.ijimpeng.2014.11.015