弹体侵彻钢筋混凝土遮弹层的阻力方程

王武 杨军 王安宝 李胜杰

王武, 杨军, 王安宝, 李胜杰. 弹体侵彻钢筋混凝土遮弹层的阻力方程[J]. 爆炸与冲击. doi: 10.11883/bzycj-2024-0217
引用本文: 王武, 杨军, 王安宝, 李胜杰. 弹体侵彻钢筋混凝土遮弹层的阻力方程[J]. 爆炸与冲击. doi: 10.11883/bzycj-2024-0217
WANG Wu, YANG Jun, WANG Anbao, LI Shengjie. Resistance equation of projectile penetrating into reinforced concrete shield[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2024-0217
Citation: WANG Wu, YANG Jun, WANG Anbao, LI Shengjie. Resistance equation of projectile penetrating into reinforced concrete shield[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2024-0217

弹体侵彻钢筋混凝土遮弹层的阻力方程

doi: 10.11883/bzycj-2024-0217
详细信息
    作者简介:

    王 武(1985- ),男,博士研究生,工程师,w-wang21@mails.tsinghua.edu.cn

    通讯作者:

    杨 军(1974- ),男,博士,研究员,junyang@tsinghua.edu.cn

  • 中图分类号: O385

Resistance equation of projectile penetrating into reinforced concrete shield

  • 摘要: 为研究弹体在侵彻钢筋混凝土受到阻力的问题,分析了现有钢筋有限长度固支梁理论模型局限,根据钢筋屈服准则研究和耗能分析,提出了弹体直接命中钢筋剪切-塑性铰链模型,以及弹体与钢筋侧面接触时的塑性弦模型,通过耗能分析得到了弹体直接阻力函数;以空腔膨胀理论模型为基础,根据弹体侵彻深度经验公式计算结果,得到了钢筋间接影响下混凝土阻力方程。通过与已有试验数据对比,验证了理论模型的合理性。通过分析钢筋屈服强度、直径、网眼尺寸等配筋方式,以及弹体命中部位对遮弹层抗侵彻性能的影响,给出了遮弹层配筋设计建议:相邻两层钢筋网错孔设置;钢筋网眼与弹体直径比值宜设为0.5~0.8;应结合钢筋极限塑性应变进行高强钢筋选择。
  • 图  1  弹体与钢筋接触方式[15]

    Figure  1.  Contact method between projectile and reinforcing bar[15]

    图  2  钢筋受力示意图

    Figure  2.  Schematic diagram of reinforcing bar under dynamic load

    图  3  尖卵头刚性弹剖面示意图

    Figure  3.  Schematic diagram of oval shaped projectile

    图  4  塑性铰等效长度

    Figure  4.  Equivalent length of plastic hinge

    图  5  塑性铰链变形示意图

    Figure  5.  Schematic diagram of plastic hinge deformation

    图  6  钢筋受弯矩作用屈服时横截面应力分布

    Figure  6.  Cross section stress distribution of reinforcing bar under bending moment action

    图  7  钢筋受弯矩和轴力共同作用屈服时横截面应力分布

    Figure  7.  Cross section stress distribution of reinforcing bar under combined bending moment and axial force

    图  8  弯矩-轴力共同作用下钢筋屈服面

    Figure  8.  Yield surface of reinforcing bar under the combined action of bending moment and axial force

    图  9  钢筋塑性变形区示意图

    Figure  9.  Schematic of plastic deformation zone of reinforcing bar

    图  10  弹体侵彻计算流程图

    Figure  10.  Flow chart of projectile penetration calculation

    图  11  侵彻试验后部分靶板及钢筋破坏形态[30]

    Figure  11.  Partial target plate and reinforcing bars failure morphology after penetration test[30]

    图  12  弹体减加速度计算结果

    Figure  12.  Calculation results of projectile deceleration

    图  13  单层钢筋网耗能计算结果

    Figure  13.  Calculation results of energy consumption for single-layer reinforcing bar mesh

    表  1  钢筋混凝土靶侵彻试验工况及结果

    Table  1.   Test conditions and results of reinforced concrete target penetration test

    靶板编号 计划撞击点位置 配筋方式/mm 弹体质量/g 弹体初速度/(m·s−1) 侵彻深度/mm
    试验结果[30] 理论计算结果 相对误差/%
    #1 网眼中心 $ \varnothing $10@75 4914 439 568 523 7.92
    #2 钢筋交叉点 $ \varnothing $10@75 4920 439 546 503 7.88
    #3 网眼中心 $ \varnothing $6.5@30 4968 430 552 517 6.34
    #4 钢筋交叉点 $ \varnothing $6.5@30 4962 431 501
    下载: 导出CSV

    表  2  弹体侵彻钢筋混凝土靶部分影响参数

    Table  2.   Impact parameters of projectile penetration into reinforced concrete targets

    γvol/% 2b/mm sh/mm sh/2a γvol/% 2b/mm sh/mm sh/mm γvol/% 2b/mm sh/mm sh/mm
    4 10 26.18 0.17 5 12 30.16 0.2 6 14 34.21 0.23
    12 37.7 0.25 14 41.05 0.27 16 44.68 0.3
    14 51.31 0.34 16 53.62 0.36 18 56.55 0.38
    16 67.02 0.45 18 67.86 0.45 20 69.81 0.47
    18 84.82 0.57 20 83.78 0.56 22 84.47 0.56
    20 104.72 0.7 22 101.37 0.68 24 100.53 0.67
    22 126.71 0.84 24 120.64 0.8 26 117.98 0.79
    24 150.8 1.01 26 141.58 0.94 28 136.83 0.91
     注:$ {\gamma }_{\text{vol}} $为体积配筋率,2b为钢筋直径,sh为钢筋网眼大小。
    下载: 导出CSV
  • [1] KENNEDY R P. A review of procedures for the analysis and design of concrete structures to resist missile impact effects [J]. Nuclear Engineering and Design, 1976, 37(2): 183–203. DOI: 10.1016/0029-5493(76)90015-7.
    [2] LI Q M, REID S R, WEN H M, et al. Local impact effects of hard missiles on concrete targets [J]. International Journal of Impact Engineering, 2005, 32(1/2/3/4): 224–284. DOI: 10.1016/j.ijimpeng.2005.04.005.
    [3] RIERA J D. Penetration, scabbing and perforation of concrete structures hit by solid missiles [J]. Nuclear Engineering and Design, 1989, 115(1): 121–131. DOI: 10.1016/0029-5493(89)90265-3.
    [4] 邓勇军, 陈小伟, 钟卫洲, 等. 弹体正侵彻钢筋混凝土靶的试验及数值模拟研究 [J]. 爆炸与冲击, 2020, 40(2): 023101. DOI: 10.11883/bzycj-2019-0001.

    DENG Y J, CHEN X W, ZHONG W Z, et al. Experimental and numerical study on normal penetration of a projectile into a reinforced concrete target [J]. Explosion and Shock Waves, 2020, 40(2): 023101. DOI: 10.11883/bzycj-2019-0001.
    [5] LUK V K, FORRESTAL M J. Penetration into semi-infinite reinforced-concrete targets with spherical and ogival nose projectiles [J]. International Journal of Impact Engineering, 1987, 6(4): 291–301. DOI: 10.1016/0734-743X(87)90096-0.
    [6] BARR P. Guidelines for the design and assessment of concrete structures subjected to impact: SRD-R-439-Issue-2 [R]. London: HMSO, 1988.
    [7] NDRC. Effects of impact and explosion: Summary Technical Report of Division 2, Vol. 1 [R]. Washington DC: National Defense Research Committee, 1946.
    [8] BERRIAUD C, SOKOLOVSKY A, GUERAUD R, et al. Local behaviour of reinforced concrete walls under missile impact [J]. Nuclear Engineering & Design, 1978, 45(2): 457–469. DOI: 10.1016/0029-5493(78)90235-2.
    [9] DANCYGIER A N. Effect of reinforcement ratio on the resistance of reinforced concrete to hard projectile impact [J]. Nuclear Engineering & Design, 1997, 172(1/2): 233–245. DOI: 10.1016/S0029-5493(97)00055-1.
    [10] CHEN X W, LI X L, HUANG F L, et al. Normal Perforation of reinforced concrete target by rigid projectile [J]. International Journal of Impact Engineering, 2008, 35(10): 1119–1129. DOI: 10.1016/j.ijimpeng.2008.01.002.
    [11] GRISARO H, DANCYGIER A N. A modified energy method to assess the residual velocity of non-deforming projectiles that perforate concrete barriers [J]. International Journal of Protective Structures, 2014, 5(3): 307–321. DOI: 10.1260/2041-4196.5.3.307.
    [12] XU X Z, MA T B, NING J G. Failure mechanism of reinforced concrete subjected to projectile impact loading [J]. Engineering Failure Analysis, 2019, 96: 468–483. DOI: 10.1016/j.engfailanal.2018.11.006.
    [13] DENG Y J, CHEN X W, SONG W J. Dynamic cavity-expansion penetration model of elastic-cracked-crushed response for reinforced-concrete targets [J]. International Journal of Impact Engineering, 2021, 157: 103981. DOI: 10.1016/j.ijimpeng.2021.103981.
    [14] LEE S, KIM C, YU Y, et al. Effect of reinforcing steel on the impact resistance of reinforced concrete panel subjected to hard-projectile impact [J]. International Journal of Impact Engineering, 2021, 148: 103762. DOI: 10.1016/j.ijimpeng.2020.103762.
    [15] 朱擎, 李述涛, 陈叶青. 配筋对超高性能混凝土抗侵彻性能的影响 [J]. 工程力学, 2023, 40(S1): 62–73,91. DOI: 10.6052/j.issn.1000-4750.2022.05.S046.

    ZHU Q, LI S T, CHEN Y Q. Influence of reinforcement on anti-penetration resistance of ultra-high-performance concrete [J]. Engineering Mechanics, 2023, 40(S1): 62–73,91. DOI: 10.6052/j.issn.1000-4750.2022.05.S046.
    [16] 张爽, 武海军, 黄风雷. 刚性弹正侵彻钢筋混凝土靶阻力模型 [J]. 兵工学报, 2017, 38(11): 2081–2092. DOI: 10.3969/j.issn.1000-1093.2017.11.001.

    ZHANG S, WU H J, HUANG F L. Resistance model of rigid projectile penetrating into reinforced concrete target [J]. Acta Armamentarii, 2017, 38(11): 2081–2092. DOI: 10.3969/j.issn.1000-1093.2017.11.001.
    [17] 黄民荣, 顾晓辉, 高永宏. 刚性弹丸侵彻钢筋混凝土的实验和简化分析模型 [J]. 实验力学, 2009, 24(4): 283–290.

    HUANG M R, GU X H, GAO Y H. Experiment and simplified analytical model for penetration of rigid projectile in a reinforced concrete target [J]. Journal of Experimental Mechanics, 2009, 24(4): 283–290.
    [18] 黄民荣. 刚性弹体对混凝土靶的侵彻与贯穿机理研究 [D]. 南京: 南京理工大学, 2011.

    HUANG M R. Penetration and perforation mechanism of rigid projectile into the concrete target [D]. Nanjing: Nanjing University of Science & Technology, 2011.
    [19] HUANG C L, WANG Z Q, LI S T, et al. Analytical model of penetration depth and energy dissipation considering impact position [J]. International Journal of Impact Engineering, 2024, 191: 104997. DOI: 10.1016/j.ijimpeng.2024.104997.
    [20] 刘志林, 孙巍巍, 王晓鸣, 等. 卵形弹丸垂直侵彻钢筋混凝土靶的工程解析模型 [J]. 弹道学报, 2015, 27(3): 84–90. DOI: 10.3969/j.issn.1004-499X.2015.03.016.

    LIU Z L, SUN W W, WANG X M, et al. Engineering analytical model of ogive-nose steel projectiles vertically penetrating reinforced concrete target [J]. Journal of Ballistics, 2015, 27(3): 84–90. DOI: 10.3969/j.issn.1004-499X.2015.03.016.
    [21] CHEN X W, LI Q M. Deep penetration of a non-deformable projectile with different geometrical characteristics [J]. International Journal of Impact Engineering, 2002, 27(6): 619–637. DOI: 10.1016/S0734-743X(02)00005-2.
    [22] PENG Y, WU H, FANG Q, et al. A note on the deep penetration and perforation of hard projectiles into thick targets [J]. International Journal of Impact Engineering, 2015, 85: 37–44. DOI: 10.1016/j.ijimpeng.2015.06.013.
    [23] 中华人民共和国住房和城乡建设部, 国家市场监督管理总局. GB/T 50081-2019 混凝土物理力学性能试验方法标准 [S]. 北京: 中国建筑工业出版社, 2019: 145–146.

    Ministry of Housing and Urban-Rural Development of the People’s Republic of China, State Administration for Market Regulation. GB/T 50081-2019 Standard for test methods of concrete physical and mechanical properties [S]. Beijing: China Architecture and Building Press, 2019: 145–146.
    [24] 黄晓莹, 陶俊林. 三种建筑钢筋材料高应变率下拉伸力学性能研究 [J]. 工程力学, 2016, 33(7): 184–189. DOI: 10.6052/j.issn.1000-4750.2014.12.1064.

    HUANG X Y, TAO J L. Tensile mechanical properties research of three construction steel bars in high strain rate [J]. Engineering Mechanics, 2016, 33(7): 184–189. DOI: 10.6052/j.issn.1000-4750.2014.12.1064.
    [25] NONAKA T. Some interaction effects in a problem of plastic beam dynamics-Part 2: analysis of a structure as a system of one degree of freedom [J]. Journal of Applied Mechanics, 1967, 34(3): 631–637. DOI: 10.1115/1.3607754.
    [26] FREW D J, HANCHAK S J, GREEN M L, et al. Penetration of concrete targets with ogive-nose steel rods [J]. International Journal of Impact Engineering, 1998, 21(6): 489–497. DOI: 10.1016/S0734-743X(98)00008-6.
    [27] FORRESTAL M J, ALTMAN B S, CARGILE J D, et al. An empirical equation for penetration depth of ogive-nose projectiles into concrete targets [J]. International Journal of Impact Engineering, 1994, 15(4): 395–405. DOI: 10.1016/0734-743X(94)80024-4.
    [28] CHEN X W, LI Q M. Deep penetration of a non-deformable projectile with different geometrical characteristics [J]. International Journal of Impact Engineering, 2002, 27(6): 619–637. DOI: 10.1016/S0734-743X(02)00005-2.
    [29] 王安宝, 邓国强, 杨秀敏, 等. 一个新的通用型侵彻深度计算公式 [J]. 土木工程学报, 2021, 54(10): 36–46. DOI: 10.15951/j.tmgcxb.2021.10.004.

    WANG A B, DENG G Q, YANG X M, et al. A new general formula for calculating penetration depth [J]. China Civil Engineering Journal, 2021, 54(10): 36–46. DOI: 10.15951/j.tmgcxb.2021.10.004.
    [30] ZHANG X Y, WU H J, ZHANG S, et al. Projectile penetration of reinforced concrete considering the effect of steel reinforcement: Experimental study and theoretical analysis [J]. International Journal of Impact Engineering, 2020, 144: 103653. DOI: 10.1016/j.ijimpeng.2020.103653.
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  • 收稿日期:  2024-07-02
  • 修回日期:  2024-09-15
  • 网络出版日期:  2024-09-19

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