A method for calculating critical spalling and perforating thicknesses of concrete slabs subjected to contact explosion
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摘要: 采用刚塑性模型描述介质的动力学行为，结合不可压缩条件和质量守恒条件及边界条件，构造塑性区的动力学许可速度场；利用极限平衡原理推导动力学许可速度场所对应的介质抗力的量纲一表达式；根据初始条件和边界条件，求解运动方程，分别得到爆炸震塌的临界厚度和爆炸贯穿的临界厚度，并推得能够反映爆炸源参数和材料参数综合性质的量纲一冲击因子。将推得的计算公式与经验公式对比分析，证明本文计算结果合理，推导的计算公式揭示了经验公式的物理本质，且具有较为广泛的适用范围。Abstract: Tanking account of the mass conservation conditions, incompressible conditions and boundary conditions, this paper described the dynamic behaviors of the medium based on the plastic-rigid model and established the compatible dynamic velocity field in the plastic zone. In addition, utilizing the limit equilibrium theory, this paper derived the equations of material resistance to explosions in both the infinite and the semi-infinite medium. Combined with the initial and boundary conditions, the equations of motion can be solved and the critical depth can be obtained. Besides, this paper has obtained a dimensionless impact factor which reflects the integrated nature of explosive sources and media. The calculated results illustrated that the critical depth and the dimensionless impact factor have a proportional relationship. Finally, the comparative analysis of the empirical formulas with the derived equations proved that our calculation methods are valid and widely applicable.
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图 1 接触爆炸下介质表面冲量荷载计算模型
Figure 1. Impulse on the surface of medium under contact explosion
图 2 半空间表面点源爆炸介质区域划分
Figure 2. Regional division of the half-space medium subjected to point-source explosion
图 5 有限厚度板表面点源爆炸介质区域划分
Figure 5. Regional division of the limited thickness slab subjected to point-source explosion
图 7 临界厚度与无量纲冲击因子的关系曲线
Figure 7. Relationship between critical thickness and dimensionless impact factor
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