A practical calculation method of steel plate concrete walls to resist perforation from missile impact in nuclear engineering
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摘要: 针对带对拉钢筋的双钢板混凝土墙，研究了双钢板混凝土墙防贯穿计算方法，建立了基于能量法的防贯穿计算公式。在已知弹体和钢板混凝土墙体材料与几何相关参数时，利用防贯穿实用计算公式可对带对拉钢筋的核工程双钢板混凝土墙体贯穿速度以及弹体剩余速度进行计算，避免了复杂的结构抗撞击反应动力时程数值分析。为验证公式的可靠性，将公式计算结果与已有刚性弹体撞击双钢板混凝土墙实验结果及其动力有限元计算结果进行对比，结果表明：防贯穿实用计算公式可以正确判断双钢板混凝土墙的贯穿状态，实用计算公式给出的弹体剩余速度与实验结果符合良好。为进一步验证公式的适用范围，将公式计算结果与共10个工况的飞机发动机撞击双钢板混凝土墙的有限元计算结果进行了对比分析，结果表明：除1个工况计算结果偏差略超10%外，其余工况的偏差均在10%以内，说明该计算方法合理可行。Abstract: The calculation method based on the energy method for resisting perforation to the SC walls with tied bars was discussed. Based on the perforation mechanism of missile impacting on the SC walls, the dissipated energy was divided into four parts: the energy dissipated by the front and rear steel plates, the energy dissipated by internal concrete and tied bars, and a practical calculation formula of preventing perforation was proposed. The perforation velocity and the residual velocity of the SC walls with tied bars can be calculated by the practical calculation formula when the related parameters of the materials and geometry about the missile and SC walls are known, thus avoiding complex impacting numerical analysis of dynamic time history. In order to verify the reliability of the formula, the results calculated through the practical formula were compared with the existing test data, as well as the dynamic finite element (FE) analysis results. The perforation state of the SC walls can be judged by the practical calculation formula concretely, and the residual velocities of the missile given by the formula are in good agreement with the test results. To further verify the application extent of the formula, the FE models about 10 cases of an aircraft engine impacting on the SC walls were established, and the solid FE models and the front closed cylindrical shell FE models of the aircraft engine were described, respectively. The results calculated through the practical formula were compared with the 10 cases of the aircraft engine impacting on the SC wall. It indicates that the deviation value of one case is slightly more than 10%. In other cases, the deviation values are all less than 10%. The accuracy and effectiveness of the proposed method can be verified.
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Key words:
- steel plate concrete (SC) walls /
- energy method /
- impact /
- perforation /
- finite element (FE) analysis
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图 1 弹体撞击带对拉钢筋的双钢板混凝土墙机理图
Figure 1. Mechanism diagram of missile impacting on SC wall with tied bars
图 2 弹体及弹-靶有限元模型（SCS-175-6T）
Figure 2. Overview of missile and missile-wall FE models (SCS-175-6T)
图 5 不同撞击速度下双钢板混凝土墙（SCS-175-4T）后钢板毁伤情况
Figure 5. Rear steel plates failure shape of SC walls at different impact velocities (SCS-175-4T)
图 6 不同撞击速度下弹体的速度时程曲线（SCS-175-4T）
Figure 6. Velocity-time curves of the missile at different impact velocities (SCS-175-4T)
表 1 钢板计算参数
Table 1. Calculation parameters of steel plate
密度${\rho _{\rm{s}}}$/(kg·m−3) 屈服强度$\sigma $ /MPa 弹性模量Es /GPa 厚度Hs/mm 无量纲参数B 应变强化指数n 7.8×103 307 210 6 1.1 0.08[10] 
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表 2 混凝土计算参数
Table 2. Calculation parameters of concrete
密度${\rho _{\rm{c}}}$/(kg·m−3) 抗压强度fc/MPa 抗拉强度设计值ft1 / MPa 厚度Hc/m 2.37×103 50.075 1.9 0.163或0.238
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表 3 公式计算及实验结果
Table 3. Formula calculation and test results
钢板 撞击速度v/(m·s−1) 贯穿速度vp/(m·s−1) 破坏形式 剩余速度vkr/ (m·s−1) 公式计算
（未考虑栓钉)公式计算
（考虑栓钉）公式计算 实验 公式计算
(未考虑栓钉)公式计算
(考虑栓钉)实验 SCS-175-6T 152.4 140.7 143.8 贯穿 贯穿 41.5 34.3 33.9 SCS-250-6T 147.7 155.0 159.7 未贯穿 未贯穿 0 0 0
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表 4 有限元模型材料（MAT003）参数
Table 4. Material parameters for FE models
组件 密度/(kg·m−3) 屈服强度/MPa 杨氏模量 /GPa 切线模量 /MPa 泊松比 侵蚀参数 失效应变 C P 钢板（6 mm） 7.8×103 307 210 603 0.3 40 5 0.28 栓钉 7.8×103 345 210 504 0.3 40 5 0.30 弹体 7.8×103 250 210 502 0.3 40 5 0.30
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表 5 数值计算和实验结果
Table 5. Numerical analysis and test results
钢板 撞击速度v/(m·s−1) 破坏形式 剩余速度vkr/(m·s−1) 有限元模拟 实验 有限元模拟 实验 SCS-175-6T 152.4 贯穿 贯穿 28.7 33.9 SCS-250-6T 147.7 鼓包 鼓包 0 0
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表 6 双钢板混凝土墙贯穿速度对比
Table 6. Comparison of perforation velocities of SC walls
钢板 贯穿速度/(m·s−1) 偏差/% 公式计算（未考虑栓钉） 公式计算（考虑栓钉） 有限元分析 未考虑栓钉 考虑栓钉 SCS-175-6T 140.7 143.8 148 −4.93 −2.84 SCS-250-6T 155.0 159.7 161 −3.73 −0.81
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表 7 飞机发动机撞击双钢板混凝土墙的贯穿速度对比
Table 7. Comparison of perforation velocities for SC walls subjected to an aircraft engine
工况 发动机类型 发动机质量/kg 发动机直径/m 发动机总长/m 混凝土墙厚度/m 贯穿速度/(m·s−1) 偏差/% 公式计算 有限元分析 C1 实心 998 0.5 0.650 0.48 128.3 126 1.83 C2 圆柱壳 998 0.5 0.650 0.48 128.3 129 −0.54 C3 实心 2 003 1.0 1.950 0.48 169.9 162 4.88 C4 圆柱壳 2 003 1.0 1.950 0.48 169.9 174 −2.36 C5 实心 4 500 1.5 3.000 0.48 166.9 151 10.53 C6 圆柱壳 4 500 1.5 3.000 0.48 166.9 159 4.97 C7 实心 8 014 2.0 4.225 0.98 178.2 178 0.11 C8 圆柱壳 8 014 2.0 4.225 0.98 178.2 187 −4.71 C9 实心 17 339 2.5 6.000 0.98 147.9 137 7.96 C10 圆柱壳 17 339 2.5 6.000 0.98 147.9 146 1.30
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