Study on failure zones and attenuation law of stress waves in concrete induced by cylindrical charge explosion
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摘要: 为了探究柱形装药爆炸应力波在混凝土介质中的传播规律,基于Karagozian and Case concrete (KCC)本构模型和多物质ALE算法(multi-material ALE,MMALE)开展数值模拟研究。首先,通过与已有的试验数据进行对比,验证了本构模型参数和数值算法的适用性;在此基础上以峰值应力为准则,对装药周围混凝土介质的爆炸破坏分区进行划分,并讨论了各破坏分区中爆炸应力波的衰减规律;之后,分析了装药长径比对爆炸破坏分区和爆炸应力波传播规律的影响;最后,进一步考虑装药埋深的影响,并建立柱形装药爆炸应力波峰值应力计算公式。研究结果表明:各爆炸破坏分区中爆炸应力波衰减规律存在显著差异,与中远区(过渡区和破裂区)相比,装药近区(拟流体区和压碎区)衰减更快,另外,柱形装药长径比增加会加快法向峰值应力的衰减;并且建立的爆炸应力波峰值应力计算公式可以较为准确快速地计算出不同形状、不同埋深下柱形装药爆炸应力波的法向峰值应力。Abstract: In blast-resistant structural design for conventional weapons, previous studies on blast-induced stress waves in solid media have predominantly focused on soil and rock media (i.e., ground shock issues), whereas research on the propagation and attenuation laws of stress waves in concrete remains relatively limited. Based on the KCC constitutive model in conjunction with the multi-material ALE (MMALE) algorithm, the propagation laws of stress waves in concrete induced by cylindrical charge explosion were numerically investigated. Firstly, the applicability of the constitutive model parameters and numerical algorithm were validated by comparing the results with the existing experiments. Subsequently, the peak stress was employed as a criterion to delineate the explosive damage zones in the concrete surrounding the charge. Additionally, the attenuation laws of explosion stress waves in each damage zone were discussed. Finally, the effect of burial depth was taken into further considered, and a formula for calculating the peak stress in concrete induced by cylindrical charge explosion was established. It was found that the attenuation patterns of blast-induced stress waves differ significantly in each explosion failure zone. The stress waves in the near-field zone (quasi-fluid and crushing zones) demonstrates a more rapid attenuation rate compared to that in the mid-field zone (transition and fracture zones). Furthermore, an increase in the aspect ratio of the cylindrical charge leads to an acceleration in the attenuation of the normal peak stress. Moreover, the established formula for calculating the peak stress of blast-induced stress waves enables accurate and rapid determination of the normal peak stress generated by cylindrical charges with varying geometries and burial depths, which can be served as a valuable reference for blast-resistant design of concrete structures.
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Key words:
- concrete /
- cylindrical charges /
- failure zones /
- explosion stress waves /
- peak stress
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ρ/(kg·m−3) D/(m·s−1) pCJ/GPa A/GPa B/GPa ω R1 R2 E/ (GJ·m−3) 1500 7450 22 625.3 23.29 0.28 5.25 1.60 8.56 ρ/(kg·m−3) C0 C1 C2 C3 C4 C5 C6 E/(MJ·m−3) 1.2929 0 0 0 0 0 0.4 0 0.25 表 3 第1组试验中各测点峰值应力的试验结果与数值模拟结果的对比
Table 3. Comparison of stress peak of tests with that of numerical simulation in the first group
测点试验值/GPa 试验平均值/GPa 数值模拟值/GPa 平均误差/% gauge 1-1 gauge 1-4 10.261 8.476 17.40 11.156 9.366 gauge 1-3 gauge 1-6 1.316 1.134 13.83 1.248 1.384 gauge 1-2 gauge 1-5 0.492 0.531 7.93 0.518 0.466 注:平均误差=(试验平均值-数值模拟值)/平均值×100% 表 4 混凝土自由场破坏分区边界尺寸及介质受力特征
Table 4. Concrete failure zone boundaries in a free field and stressed medium properties
破坏分区类型 边界尺寸/(mkg1/3) 混凝土介质受力特征 近流体区 0.08~0.13 混凝土受强间断冲击波作用,其峰值应力远大于混凝土剪切强度,介质呈塑性流动状态 压碎区 0.13~0.17 爆炸应力值远大于混凝土抗压强度,介质被完全压碎 过渡区 0.17~0.46 混凝土介质受环向和径向压力共同作用,发生压剪破坏,裂隙呈网状分布 破裂区 0.46~1.0 混凝土介质主要受环向拉应力作用,发生拉伸破坏,形成径向裂隙 弹性区 ≥ 1.0 介质未发生塑性变形,处于弹性状态 表 5 不同长径比的柱形装药各破坏分区参数
Table 5. Parameters for different length-to-diameter ratios of cylindrical charges in each failure zone
l/d 分区 Z/(m/kg1/3) k n R2 2 近流体区 0.10~0.15 1.70×10−3 3.59 0.9937 压碎区 0.15~0.18 6.05×10−4 3.96 0.9862 过渡区 0.18~0.44 2.03×10−2 1.98 0.9943 破裂区 0.44~1.00 3.28×10−2 1.47 0.9991 4 近流体区 0.14~0.17 1.82×10−4 5.25 0.9945 压碎区 0.17~0.20 1.69×10−5 6.59 0.9780 过渡区 0.20~0.42 1.62×10−2 2.24 0.9891 破裂区 0.42~1.00 3.16×10−2 1.52 0.9991 6 近流体区 0.17~0.20 4.88×10−5 6.61 0.9964 压碎区 0.20~0.22 1.34×10−6 8.83 0.9705 过渡区 0.22~0.40 1.16×10−2 2.66 0.9826 破裂区 0.40~1.00 3.05×10−2 1.59 0.9985 8 近流体区 0.20~0.23 6.66×10−6 8.49 0.9897 压碎区 0.23~0.25 5.39×10−7 10.15 0.9773 过渡区 0.25~0.40 9.30×10−3 2.97 0.9783 破裂区 0.40~1.00 2.85×10−2 1.67 0.9975 -
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