Test and numerical study on the near-field explosion response of reinforced concrete box girder
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摘要: 为了研究近场爆炸作用下单箱三室混凝土箱梁的动力响应和破坏特征，开展了缩比试件爆炸试验和数值模拟。以原型桥梁主梁截面按1∶3缩比设计和制作了箱梁试件，测量了3 kg TNT药柱爆炸作用下试件的反射超压、钢筋应变、竖向位移及破洞形态；采用LS-DYNA软件进行了箱梁爆炸响应模拟，结合试验数据验证了数值模拟方法的可靠性；分析了TNT当量、起爆位置、混凝土强度、配筋率对箱梁抗爆性能的影响。结果表明：3 kg TNT药柱于箱梁中间箱室中心正上方0.4 m处起爆时，在中间箱室顶板中心形成一个椭圆形的贯穿破口，破口沿横、纵桥向长度分别为41.50、45.50 cm；中间箱室顶板底面的混凝土发生大面积剥落，呈现喇叭状冲切破坏特征；多室箱梁的超宽截面形式使得其爆炸响应沿横桥向分布不均匀；箱梁底板竖向位移峰值和钢筋应变峰值随药量的增大而增大，采用最小二乘法得到了对应的拟合曲线表达式；不同起爆位置下，中间箱室底板中心的竖向位移均大于两侧箱室中心的。Abstract: In order to study the dynamic response and failure characteristics of the concrete girder with single box and three chambers under near-field explosion, the explosion test and numerical simulation of a scaled specimen were carried out. The girder specimen was designed and manufactured by the scale of 1∶3 according to the prototype bridge girder. The bottom of the specimen was supported by six brick supports. The TNT grain was located at 0.4 m above the top plate center of the middle chamber with an equivalent of 3 kg and a proportional distance of 0.77 m/kg1/3. The reflected overpressure, reinforcement strain, vertical displacement and acceleration of bottom plate and the shape of breach were measured and analyzed. The effectiveness of the explosion load in the test was verified by comparing the measured reflection overpressure with the calculated value by the CONWEP empirical formula. The LS-DYNA software was used to simulate the explosion response of the box girder. The SOLIDWORKS software and HYPERMESH software were used to establish the finite element model of the specimen. The Solid 164 element was used to simulate the concrete, and Beam 188 element was used to simulate the steel rebar. The LOAD BLAST ENHANCED (LBE) method was used to apply explosive loads. The *MAT_CONCRETE_DAMAGE_REL3 material model and *MAT_PLASTIC_KINEMATIC model were used to simulate the concrete and rebar, respectively, to consider the effects caused by high strain and large deformation. The keyword *MAT_ADD_EROSION was used to define the failure of concrete. The reliability of numerical simulation method was verified with the test data. Finally, the effects of TNT equivalent, detonation location, concrete strength, and reinforcement ratio on the explosion resistance of the box girder were analyzed. The results show that when a TNT grain of 3 kg is detonated at 0.4 m above the center of the middle chamber of the box girder, an elliptical penetration breach is formed in the center of top plate of the middle chamber, with the length values along the transverse and longitudinal bridge directions being 41.50 and 45.50 cm, respectively. The concrete on the bottom surface of the top plate of the middle chamber peels off in a large area, presenting a trumpet-shaped punching failure feature. The extra-wide cross-section of multi-chamber box girder makes the explosive responses unevenly distributing along the transverse bridge direction. The peak values of vertical displacement and rebar strain of the bottom plate of the girder increase with the increase of the charge. Using the least square method, the corresponding fitting curve expressions are obtained. Under the working conditions of different detonation positions, the vertical displacement of the bottom plate center of the middle chamber is greater than those of the chamber centers on both sides. The results can provide a basis for the anti-explosive evaluation and protection of similar extra-wide concrete box girder.
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图 5 压力、加速度及位移测点布置
Figure 5. Layout of measuring points of pressure, acceleration and displacement
图 6 爆炸冲击波反射超压对比
Figure 6. Comparison of reflected overpressures of explosion shock wave
图 8 各箱室底板中心竖向位移时程曲线试验结果
Figure 8. Measured time history curves of vertical displacement at bottom plate center of each chamber
图 9 钢筋应变时程曲线试验结果
Figure 9. Test results of time history curve on reinforcement strains
图 10 箱梁底板加速度时程曲线试验结果
Figure 10. Test results of acceleration time history curve of box girder bottom plate
图 12 箱梁试件损伤形态的试验与数值模拟对比
Figure 12. Comparison of test and numerical simulations on damage morphology of box girder specimens
图 13 不同比例爆距下箱梁的损伤形态云图
Figure 13. Damage morphology of box girder under different proportional blast distances
图 14 不同比例爆距下箱梁底板中心竖向位移时程曲线
Figure 14. Time history curves of vertical displacement at the center of bottom plate of the box girder under different proportional blast distances
图 15 不同比例爆距下箱梁底板中心钢筋应变时程曲线
Figure 15. Time history curves of the reinforcement strain at the center of bottom plate of the box girder under different proportional blast distances
图 16 箱梁底板中心竖向位移峰值和钢筋应变峰值与药量关系的拟合曲线
Figure 16. Fitting curves of the relationships between the peak vertical displacement and rebar strain of the bottom plate center of the girder and the charge amount
图 17 不同混凝土抗压强度下箱梁底板中心的位移时程曲线
Figure 17. Time history curves of box girder bottom plate center displacement at different concrete compressive strengths
图 18 不同配筋率下箱梁底板中心位移时程曲线
Figure 18. Time history curves of box girder bottom plate center displacement at different reinforcement ratios
图 19 不同起爆位置下箱梁的损伤形态云图
Figure 19. Damage morphologies of box girders varied with different initiation positions
图 20 工况1～3作用下箱梁底板的竖向位移时程曲线
Figure 20. Time history curves of vertical displacements of box girder bottom under conditions 1−3
表 1 箱梁爆炸试验测点说明
Table 1. Description of measuring points for explosion test of box girder
测点类别 测试内容 测试方式 测点数量 SR 钢筋应变 BE120-6AA-X 30型电阻应变片 12 PC 反射超压 PVDF压电薄膜 3 DC 加速度 YK-0003pc型加速度传感器 3 AC 竖向位移 WYL33型位移传感器 3 
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表 2 混凝土材料参数
Table 2. Material parameters of concrete
参数 ρ/(kg·m−3) A0/MPa RSIZE UCF LCRATE 数值 2300 −30 39.37 1.45×10−4 −1 注：ρ为材料密度；A0为最大剪切破坏面参数，根据混凝土立方体抗压强度测试结果取值；RSIZE、UCF、LCRATE为LS-DYNA软件中的选项卡名称。其中，RSIZE代表长度单位的转换系数；UCF为应力单位的转化系数；LCRATE表示应变率曲线调用类型，若输入−1，LS-DYNA软件将自动生成并调用应变率曲线；若输入任一正值，则采用用户自定义的应变率曲线。
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表 3 钢筋材料参数
Table 3. Material parameter of reinforcement
ρ/(kg·m−3) E/Pa ν σY/Pa Et/Pa β C P εF 7800 2×1011 0.3 4.68×108 2.1×109 0 40 5 0.1 注：ρ为材料密度；E为弹性模量；ν为泊松比；σY为屈服应力；Et为切线模量；β为硬化参数，根据不同情况取0、1，各项同性（β=1）、随动硬化（β=0）、混合硬化（0<β<1）；C、P为适用于Cowper-Symonds应变率模型的参数；εF为侵蚀单元的失效应变；VP为LS-DYNA软件中的选项卡名称，代表速率效应公式的调用编号，输入0表示考虑比例屈服应力，输入1表示考虑黏塑性应变率效应。
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表 4 不同网格尺寸下箱梁混凝土破口长度和竖向位移对比
Table 4. Comparison of concrete breach length and vertical displacement of girder under different mesh sizes
网格尺寸/mm 顶板破口长度/cm 破口长度误差比/% 底板竖向位移/mm 位移误差比/% 沿长边方向 沿短边方向 沿长边方向 沿短边方向 试验值 41.50 45.50 − − 19.26 − 20 45.54 42.72 9.73 −6.11 21.35 10.85 30 45.95 45.22 10.72 −0.62 21.60 12.15 40 47.66 48.55 14.80 6.70 22.05 14.49
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表 5 不同药量下箱梁混凝土破口长度和竖向位移对比
Table 5. Comparison of concrete breach length and vertical displacement of girder under different TNT equivalents
药量/kg 爆心位置 爆高/m 比例爆距/(m∙kg−1/3) 贯穿破口长度/cm 竖向位移峰值/mm 沿长边方向 沿短边方向 0.3 箱室2中心 0.4 0.598 即将贯穿 即将贯穿 4.51 1 箱室2中心 0.4 0.400 12.98 12.81 9.82 3 箱室2中心 0.4 0.277 45.95 45.22 21.60 5 箱室2中心 0.4 0.234 59.65 58.18 32.18 8 箱室2中心 0.4 0.200 70.79 71.10 61.39 10 箱室2中心 0.4 0.186 79.43 77.63 82.88
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表 6 工况设计
Table 6. Working condition design
工况 TNT当量/kg 爆心位置 爆心高度/m 比例爆距/(m∙kg−1/3) 1 3 箱室1顶板中心正上方 0.4 0.28 2 3 箱室2顶板中心正上方 0.4 0.28 3 3 箱室3顶板中心正上方 0.4 0.28
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