Numerical simulation on dynamic response of reinforced concrete beams to secondary explosion
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摘要: 为了探究钢筋混凝土梁在二次爆炸作用下的毁伤效应，开展了相关数值分析研究：利用LS-DYNA中的流固耦合算法和完全重启动技术，对钢筋混凝土梁二次爆炸试验进行了数值模拟，分析结果与试验结果基本一致，验证了模拟方法和材料模型参数的正确性；在此基础上，对二次爆炸场景进行扩展，对典型足尺钢筋混凝土梁进行建模分析，探究了爆炸场景、混凝土强度、纵筋配筋率和箍筋配筋率对二次爆炸作用下钢筋混凝土梁损伤破坏模式和动力响应的影响。结果表明：由于压力膜效应的存在，在保持爆炸总当量不变的前提下，单次爆炸对钢筋混凝土梁构件造成的损伤比连续两次爆炸造成的累积损伤更严重；提高混凝土强度可以显著提高二次爆炸作用下钢筋混凝土梁的抗爆性能；提高纵筋配筋率对梁抗爆性能的提升效果不明显；而对混凝土梁支座部位采用箍筋加密措施可以降低钢筋混凝土梁在爆炸作用下的剪切破坏程度，提高钢筋混凝土梁在二次爆炸作用下的抗爆性能。进一步计算得到了所涉及二次爆炸场景下两种不同设计参数钢筋混凝土梁的等损伤曲线，建立了相应的损伤程度分区图。Abstract: Terrorist attacks and local wars occur frequently, which makes the risk of buildings subjected to multiple explosions increasing. Most of the existing research focuses on the single explosion scenario, and there are few studies on the damage effect of reinforced concrete structures under multiple explosions. In order to study the damage effect of reinforcement concrete beams under secondary explosion and offset the shortcomings of the existing research, relevant numerical analysis was carried out. The damage parameters of the K&C concrete constitutive model were modified firstly. And the arbitrary Lagrangian-Eulerian method for fluid-structure interaction was used to simulate the secondary explosion experiment of reinforced concrete beam with the full restart function of LS-DYNA. The numerical analysis results were well consistent with the test results, verifying the effectiveness of the simulation method and the modified constitutive model. On this basis, the secondary explosion simulation conditions were expanded. The effects of various parameters, including scaled distance, concrete compressive strength, longitudinal reinforcement ratio and transverse reinforcement details, on the damage effect of typical size reinforcement concrete beams under secondary explosion were further analyzed. The results show that due to the compressive membrane action of reinforcement concrete beam, keeping the total equivalent TNT weight of the explosion unchanged, the damage of RC component caused by one single explosion is more serious than the cumulative damage caused by two successive explosions. The concrete compressive strength has a more significant effect on the blast resistance performance of RC beams under secondary explosion, the higher the concrete strength, the lower the damage degree of the beam under the secondary explosion. Increasing the longitudinal reinforcement ratio has no obvious effect on improving the blast resistance performance of the beam and reducing the transverse reinforcement spacing can effectively decrease the shear failure degree of reinforcement concrete beam which makes the blast resistance performance of RC beams under secondary explosion and near explosion improved. The iso-damage curves of reinforcement concrete beams with two different design parameters are further calculated and the corresponding damage degree zoning maps are established.
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Key words:
- reinforced concrete /
- blast load /
- secondary explosion /
- fluid-structure interaction /
- dynamic response
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图 1 K&C默认损伤曲线与修正后损伤曲线对比
Figure 1. Comparison of damage function between the K&C model default and modified parameters
图 6 试验和有限元计算的得到梁跨中挠度时程曲线对比
Figure 6. Comparisons of deflection time history at mid-span between experiment and numerical simulation
图 13 爆炸荷载作用下典型钢筋混凝土构件压力膜效应
Figure 13. Compression membrane action in a typical reinforced concrete member under blast loading
图 14 总当量相同时单次爆炸作用和二次爆炸作用损伤云图对比
Figure 14. The damage contours of single explosion and secondary explosion under the same total TNT equivalent
图 15 梁跨中位移时程曲线：Beam4~Beam7
Figure 15. Deflection time history at mid-span: Beam4−Beam7
图 17 RC梁Beam4～Beam7在二次爆炸作用下的损伤云图
Figure 17. The damage contours of Beam4−Beam7 under secondary explosion
图 18 比例距离为0.141 m/kg1/3时RC梁Beam8～Beam11损伤云图
Figure 18. Damage contours of Beam8−Bema11 with the scaled distance of 0.141 m/kg1/3
图 19 梁跨中位移时程曲线：Beam8~Beam11
Figure 19. Deflection time history at mid-span: Beam8−Beam11
图 21 梁跨中位移时程曲线：Beam4、Beam12、Beam13
Figure 21. Deflection time history at mid-span: Beam4, Beam12 and Beam13
图 22 梁跨中位移时程曲线：Beam4、Beam14～Beam16
Figure 22. Deflection time history at mid-span: Beam4, Beam14−16
图 24 Beam4，Beam14~Beam16支座反力时程曲线
Figure 24. Reaction force time history of Beam4, Beam14−Beam16 under secondary explosion
图 25 梁跨中位移时程曲线：Beam8、Beam17、Beam18
Figure 25. Deflection time history at mid-span: Beam8, Beam17 and Beam18
图 26 比例距离为0.141m/kg1/3时RC梁Beam8、Beam17、Beam18损伤云图
Figure 26. The damage contours of Beam8, Bema17 and Beam18 with scaled distance 0.141m/kg1/
图 27 不同损伤程度阈值下钢筋混凝土梁二次爆炸等损伤曲线
Figure 27. The iso-damage curves of RC beams under secondary explosion with different damage levels
图 28 二次爆炸作用下钢筋混凝土梁损伤程度分区图
Figure 28. Zoning map of the damage degree of the RC beams under secondary explosion
表 1 参数(η, λ)具体取值
Table 1. Damage parameters (η, λ) of K&C model
上升段 下降段 λ η λ η 0 0 1.70×10−4 0.73617 8.00×10−6 0.37026 3.00×10−4 0.54456 2.40×10−5 0.81341 5.50×10−4 0.37119 4.00×10−5 0.97668 1.00×10−3 0.24346 5.60×10−5 1.00000 1.65×10−3 0.16694 2.50×10−3 0.12059 3.50×10−3 0.09209 1.00×10−2 0.03876 
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表 2 MAT_HIGH_EXPLOSIVE_BURN材料模型及EOS_JWL状态方程输入参数
Table 2. Input parameters for MAT_HIGH_EXPLOSIVE_BURN and EOS_JWL
密度/(kg·m−3) 爆速/(m·s-1) 爆压/Pa A/Pa B/Pa R1 R2 ω E0/Pa 初始相对体积 1630 6930 2.1×1010 3.712×1011 3.23×109 4.15 0.95 0.32 7×109 1
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表 3 MAT_NULL材料模型及EOS_LINEAR_POLYNOMIAL状态方程输入参数
Table 3. Input parameters for MAT_NULL and EOS_LINEAR_POLYNOMIAL
密度/(kg·m−3) 粘滞系数/(Pa·s) C0, C1, C2, C3, C6 C4, C5 E0/Pa 初始相对体积 1.29 2×10−5 0 0.4 2.5×105 1
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表 4 足尺钢筋混凝土梁设计参数及爆炸工况
Table 4. The details of the full-size RC beams and the explosive scenarios
编号 (装药量/kg, 爆距/m) 混凝土强度等级 纵筋 箍筋 第1次 第2次 Beam1 (45, 2) (45, 2) C30 3 14
8@200mm
Beam2 (90, 2) (45, 2) C30 3 Beam3 (135, 2) (45, 2) C30 3 Beam4 (45, 1) (45, 1) C30 3 Beam5 (45, 1) (45, 1) C40 3 Beam6 (45, 1) (45, 1) C50 3 Beam7 (45, 1) (45, 1) C60 3 Beam8 (45, 0.5) − C30 3 Beam9 (45, 0.5) − C40 3 Beam10 (45, 0.5) − C50 3 Beam11 (45, 0.5) − C60 3 Beam12 (45, 1) (45, 1) C30 3 Beam13 (45, 1) (45, 1) C30 3 Beam14 (45, 1) (45, 1) C30 3 梁端箍筋加密 Beam15 (45, 1) (45, 1) C30 3 梁端箍筋加密 Beam16 (45, 1) (45, 1) C30 3 Beam17 (45, 0.5) − C30 3 梁端箍筋加密 Beam18 (45, 0.5) − C30 3 梁端箍筋加密
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表 5 RC梁损伤的计算结果
Table 5. Numerical results of RC-beams damage
编号 爆次 Xm/mm θmax/(°) 损伤程度 编号 爆次 Xm/mm θmax/(°) 损伤程度 Beam1 二次 7.562 0.271 轻度损伤 Beam10 单次 182.493 6.507 完全破坏 Beam2 二次 8.214 0.294 轻度损伤 Beam11 单次 143.675 5.131 完全破坏 Beam3 二次 15.188 0.544 轻度损伤 Beam12 二次 44.363 1.588 中度损伤 Beam4 二次 43.522 1.558 中度损伤 Beam13 二次 38.934 1.394 中度损伤 Beam5 二次 35.765 1.281 中度损伤 Beam14 二次 42.670 1.528 中度损伤 Beam6 二次 32.488 1.163 中度损伤 Beam15 二次 37.709 1.350 中度损伤 Beam7 二次 27.713 0.992 轻度损伤 Beam16 二次 35.057 1.255 中度损伤 Beam8 单次 254.972 9.054 完全破坏 Beam17 单次 235.966 8.389 完全破坏 Beam9 单次 215.498 7.671 完全破坏 Beam18 单次 201.104 7.164 完全破坏
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表 6 两种方法得到二次爆炸作用下梁的跨中最大位移和支座最大转角计算结果
Table 6. Numerical results of maximum midspan displacement and maximum bearing rotation angle by ALE and CONWEP
梁编号 跨中最大位移/mm 支座最大转角/(°) 梁编号 跨中最大位移/mm 支座最大转角/(°) ALE CONWEP ALE CONWEP ALE CONWEP ALE CONWEP Beam4 43.522 46.933 1.558 1.680 Beam7 27.713 29.761 0.992 1.066 Beam5 35.765 38.608 1.281 1.382 Beam14 42.670 43.524 1.528 1.558 Beam6 32.488 33.628 1.163 1.204 Beam15 37.709 40.237 1.350 1.441
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表 7 不同损伤阈值下等损伤曲线计算参数
Table 7. Calculation parameters of iso-damage curves under different damage levels
BeamA BeamB θmax/
(°)a1/
(m·kg−1)a2/
(m·kg−2)b/m θmax/
(°)a1/
(m·kg−1)a2/
(m·kg−2)b/m 1 0.01766 −8.81×10−6 1.4724 1 0.01194 −5.28×10−6 1.1229 2 0.01105 −4.77×10−6 0.8542 2 0.00898 −4.05×10−6 0.5772 4 0.00926 −4.26×10−6 0.4573 4 0.00808 −4.47×10−6 0.4493
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