近场近地爆炸下建筑柱爆炸荷载分布规律及简化模型

喻君 刘福余 方秦

喻君, 刘福余, 方秦. 近场近地爆炸下建筑柱爆炸荷载分布规律及简化模型[J]. 爆炸与冲击, 2024, 44(1): 015201. doi: 10.11883/bzycj-2022-0366
引用本文: 喻君, 刘福余, 方秦. 近场近地爆炸下建筑柱爆炸荷载分布规律及简化模型[J]. 爆炸与冲击, 2024, 44(1): 015201. doi: 10.11883/bzycj-2022-0366
YU Jun, LIU Fuyu, FANG Qin. Distribution pattern and simplified model of blast load for building columns under near-field near-ground explosion[J]. Explosion And Shock Waves, 2024, 44(1): 015201. doi: 10.11883/bzycj-2022-0366
Citation: YU Jun, LIU Fuyu, FANG Qin. Distribution pattern and simplified model of blast load for building columns under near-field near-ground explosion[J]. Explosion And Shock Waves, 2024, 44(1): 015201. doi: 10.11883/bzycj-2022-0366

近场近地爆炸下建筑柱爆炸荷载分布规律及简化模型

doi: 10.11883/bzycj-2022-0366
基金项目: 国家自然科学基金(51978246);中央高校基本科研业务费与专项资金(2242022R10073)
详细信息
    作者简介:

    喻 君(1982- ),男,博士,教授,junyu@seu.edu.cn

  • 中图分类号: O383; O384

Distribution pattern and simplified model of blast load for building columns under near-field near-ground explosion

  • 摘要: 为了快速评估近场近地爆炸荷载下建筑柱的动力响应和破坏模式,通过数值仿真方法,探究了近场近地爆炸工况下冲击波在建筑柱迎爆面的分布规律,并提供了该工况下的爆炸荷载简化模型。为此,首先利用已有实验数据验证数值模型,并建立典型近地近场爆炸工况的数值模型,然后研究比例爆距和比例爆高对建筑柱冲击波特征参数的影响规律,最后拟合出柱迎爆面反射冲量和正相超压持续时间的计算公式,将柱迎爆面各点爆炸荷载转化为等效三角形荷载模型,为工程实践中建筑柱遭受近场近地爆炸作用下的抗爆设计提供荷载输入。研究结果表明:当比例爆高小于0.3 m/kg1/3、比例爆距在0.4~0.6 m/kg1/3范围时,最大反射冲量沿柱高可简化为三折线分布;当比例爆距在0.6~1.4 m/kg1/3范围时,最大反射冲量沿柱高可近似简化为双折线分布;在同一比例爆距和比例爆高工况下,随着炸药当量的增加,柱迎爆面相同比例高度处反射超压峰值保持不变而反射冲量正比于当量的立方根。
  • 图  1  实验设置

    Figure  1.  Experimental set-up

    图  2  参照实验对应的有限元模型

    Figure  2.  Finite element models for reference tests

    图  3  近场近地球形炸药爆炸荷载数值模型(单位:mm)

    Figure  3.  Numerical model of blast load generated by spherical charges under near-field near-ground scenarios (unit: mm)

    图  4  基于柱表面反射超压的数值模型参数敏感性分析(η为网格尺寸大小)

    Figure  4.  Sensitivity analysis of numerical model parameters in accordance with overpressure at the front face of the columns (η is the element size)

    图  5  沿柱高的冲击波传播过程(底部传播情况)

    Figure  5.  Shock wave propagation along the column length (propogation at the bottom of the column)

    图  6  沿柱高的冲击波传播过程(中部传播情况)

    Figure  6.  Shock wave propagation along the column length (propogation at the middle of the column)

    图  7  沿柱高的冲击波传播过程(顶部传播情况)

    Figure  7.  Shock wave propagation along the column length (propogation near the top of the column)

    图  8  柱迎爆面最大反射冲量分布

    Figure  8.  Distribution of the maximum reflected impulse at the front face of the column

    图  9  最大反射冲量分布简化模型

    Figure  9.  Simplified models of the maximum reflected impulse distribution

    图  10  关键冲量的拟合结果

    Figure  10.  Fitting results of critical impulses

    图  11  冲量沿柱截面宽度的横向分布简化

    Figure  11.  Simplification of impulse distribution in transverse direction along the column width

    图  12  正相持续时间t0与最大反射冲量沿柱高的分布及t0的拟合结果

    Figure  12.  Distribution of the positive phase duration (t0) and the maximum reflected impulse (Ir) along the colume height and the fitting result of t0 at the detonation height

    图  13  不同柱高处反射超压时程曲线

    Figure  13.  Time-histories of reflected overpressure at different column heights

    图  14  炸药相似比对超压、冲量和超压时程的影响(Z=0.6 m/kg1/3, Hc/W1/3=0.1 m/kg1/3

    Figure  14.  Influence of λ on peak overpressure, maximum reflected impulse and time history of overpressure (Z=0.6 m/kg1/3, Hc/W1/3=0.1 m/kg1/3)

    图  15  炸药相似比对超压、冲量和超压时程的影响(Z=0.6 m/kg1/3, Hc/W1/3=0.3 m/kg1/3

    Figure  15.  Influence of λ on overpressure, impulse and overpressure time history(Z=0.6 m/kg1/3, Hc/W1/3=0.3 m/kg1/3

    图  16  双折线模型对比验证

    Figure  16.  Verification of the bilinear model by the maximum reflected impulse

    图  17  三折线模型对比验证

    Figure  17.  Verification of the trilinear model by the maximum reflected overpressure

    表  1  Woodson实验工况表[18]

    Table  1.   Woodson’s experimental cases[18]

    工况 结构 mC4/kg mTNT/kg R/m Z/(m·kg−3)
    实验1 无填充墙 7.1 9.6 1.52 0.72
    实验2 无填充墙 7.1 9.6 1.07 0.50
    实验3 全填充墙 7.1 9.6 1.07 0.50
    实验4 含窗填充墙 7.1 9.6 1.07 0.50
    实验5 车库 7.1 9.6 1.07 0.50
     注:m为质量,C4是实验所使用炸药,模拟使用TNT炸药,当量转化系数取1.35;Z为比例爆距;R为爆距。
    下载: 导出CSV

    表  2  Liu实验工况[19]

    Table  2.   Liu’s experimental cases[19]

    工况 TNT/kg R/m Hc/m Z/(m·kg−3) Rso/m
    1 1 3 1.05 3.00 2
    2 2 3 1.05 2.38 2
    3 4 2 1.05 1.89 2
     注:R为炸药中心到柱等高位置处的爆距;Hc为爆心距地表高度;Rso为自由场超压传感器布置距离;Z为比例爆距。
    下载: 导出CSV

    表  3  Woodson实验[18]爆炸荷载的模拟结果与实测值对比

    Table  3.   Comparisons of numerical values and Woodson’s experimental[18] results

    工况 测点 pr/MPa Ir/(kPa∙s) 误差/% 工况 测点 pr/MPa Ir/(kPa∙s) 误差/%
    实测[18] 模拟 实测[18] 模拟 pr Ir 实测[18] 模拟 实测[18] 模拟 pr Ir
    实验1 BC1 8.32 12.17 1.04 1.10 46.27 5.77 实验3 BC1 15.05 16.61 3.02 3.43 10.37 13.58
    BC2 0.40 0.56 0.24 0.19 40.00 −20.83 BC2
    BC3 9.36 6.23 1.22 1.02 −33.44 −16.39 BC3 9.57 15.67 1.71 2.28 63.74 33.33
    实验2 BC1 11.52 12.53 2.77 2.38 8.77 −14.08 实验5 BC1 11.52 12.53 2.33 2.38 8.77 2.15
    BC2 0.66 0.47 −28.79 BC2 0.66 0.47 −28.79
    BC3 10.41 15.23 1.23 1.67 46.30 35.77 BC3 10.41 15.23 1.48 1.67 46.30 12.84
     注:pr为超压,Ir为冲量;所有超压和冲量模拟误差的算术平均值为16.32%和5.79%。
    下载: 导出CSV

    表  4  Liu实验[19]超压模拟结果与实测值对比

    Table  4.   Comparison of numerical predictions and Liu’s experimental[19] results

    测点 Case 1超压/MPa 误差/% 测点 Case 2超压/MPa 误差/% 测点 Case 3超压/MPa 误差/%
    实测 模拟 实测 模拟 实测 模拟
    so 0.21 0.12 −42.86 ry2 0.31 0.23 −25.81 ry2 0.52 0.57 9.62
    ry3 0.14 0.15 7.14 ry3 0.43 0.21 −51.16 ry3 0.77 0.84 9.09
    rb3 0.06 0.03 −50.00 ry4 0.39 0.23 −41.03 ry4 0.50 0.57 14.00
    rb3 0.08 0.04 −50.00 so 0.74 0.82 10.81
    平均 −28.57 −42.00 10.88
     注:三个工况超压模拟误差的算术平均值为−19.90%
    下载: 导出CSV

    表  5  反射冲量沿柱高分布特征及简化模型

    Table  5.   Distribution characteristics and simplified models of reflected impulse along column length

    爆心高度(Hc/W1/3分布特征及简化模型
    小比例爆距(0.4≤Z/(m∙kg−1/3)≤0.6)大比例爆距(0.6<Z/(m∙kg−1/3)≤1.4)
    小比例爆高(≤0.3 m/kg1/3“1/x函数形分布”,可简化为三折线模型柱底“针状峰值”分布,可简化为双折线模型
    大比例爆高(>0.3 m/kg1/3“局部峰值”归为局部突变分布,建议通过数值方法确定荷载线性分布,可简化为双折线模型
    下载: 导出CSV

    表  6  反射冲量拟合计算公式的参数取值

    Table  6.   Coefficients of regressed formula for reflected impulse calculation

    i a b c d
    Ir-b 1.9833 −1.4980 0.0062 −2.2080
    Ir-m/Ir-b 0.4690 0.9709 −0.0068 −1.3546
    Ir-t/Ir-b 0.3440 0.7766 −0.0491 −0.5805
    Ir-a/Ir-b 0.8792 0.4335 −0.0126 −1.4213
    下载: 导出CSV

    表  7  不同高度处最大反射冲量横向分布($Z=0.4\;{\mathrm{m/kg}}^{1/3},\;H_{\mathrm{c}}/W^{1/3}=0.1\;{\mathrm{m/kg}}^{1/3} $

    Table  7.   Transverse distribution of the maximum impulse at different column heights ($Z=0.4\;{\mathrm{m/kg}}^{1/3},\;H_{\mathrm{c}}/W^{1/3}=0.1\;{\mathrm{m/kg}}^{1/3} $)

    h/mmImid/(kPa∙s)Iedg/(kPa∙s)Iedg/Imid
    2006.546.060.93
    7002.252.110.94
    12000.630.620.98
    17000.350.350.99
    22000.120.110.94
     注:Imid为中轴线最大反射冲量,Iedg为柱边缘最大反射冲量。
    下载: 导出CSV

    表  8  双折线与三折线模型冲量误差比较

    Table  8.   Comparison of fitting results and numerical predictions

    h/m 冲量/(kPa·s) 误差/%
    双折线 三折线
    模拟值 公式计算值 模拟值 公式计算值 双折线 三折线
    0 2.52 2.41 7.09 6.37 −4.37 −10.16
    0.5 1.90 1.91 3.16 2.27 0.52 −28.17
    1.0 1.25 1.43 1.60 1.46 14.40 −8.75
    1.5 0.94 0.94 0.88 0.66 0.00 −25.00
    2.0 0.68 0.8 0.54 0.49 17.65 −9.26
    平均误差 5.64 −16.27
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-07-02
  • 修回日期:  2022-10-08
  • 网络出版日期:  2022-10-14
  • 刊出日期:  2024-01-11

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