Distribution pattern and simplified model of blast load for building columns under near-field near-ground explosion
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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。Abstract: To rapidly assess the dynamic responses and failure modes of the building columns under near-field near-ground explosions, in this paper numerical simulation method is employed to investigate the distribution pattern of the shock waves that are applied on the front face of building columns under near-field near-ground blast scenarios, and a corresponding simplified blast load model is proposed. To this end, firstly, the existing experimental data of overpressure and impulse were selected to validate the numerical model for blast load. Then, a typical numerical model under near-field near-ground blast scenarios was established to study the effects of the scaled distance and the scaled height of spherical charges on the characteristic values of the shock waves acting at the building columns. Finally, formulae for the maximum reflected impulse and the representative value of the positive overpressure duration were derived based on nonlinear regression analysis, and the blast load at each location of the column front face was represented by an equivalent triangular load model. The results indicate that when the scaled height of the charge is less than 0.3 m/kg1/3, the distribution of the maximum reflected impulse along the column length can be represented as a trilinear model and a bilinear model for the scaled distance of 0.4−0.6 m/kg1/3 and 0.6−1.4 m/kg1/3, respectively. In comparison, the distribution of the shock waves in the transverse direction of a column section was approximately uniform. Moreover, under a given scaled distance and a scaled height, the peak reflected overpressure remains constant as the charge weight increases, but the maximum reflected impulse is proportional to the cubic root of the charge weight at the locations with the identical scaled height of the column.
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Key words:
- building column /
- near-field blast /
- near-ground blast /
- blast load /
- load model
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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 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
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。 
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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。
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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%。
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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%
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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
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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
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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/mm Imid/(kPa∙s) Iedg/(kPa∙s) Iedg/Imid 200 6.54 6.06 0.93 700 2.25 2.11 0.94 1200 0.63 0.62 0.98 1700 0.35 0.35 0.99 2200 0.12 0.11 0.94 注：Imid为中轴线最大反射冲量，Iedg为柱边缘最大反射冲量。
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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
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