Numerical study on dynamic response and spall damage of filter concrete under impact load
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摘要: 借鉴局域共振材料的工作机制，通过在混凝土基体中嵌入滤波单元，设计出具有应力波衰减特性的滤波混凝土。通过将滤波混凝土结构简化为质量弹簧力学系统来分析滤波混凝土对应力波的衰减机制。采用数值模拟方法，对比研究了冲击荷载作用下普通混凝土模型和滤波混凝土模型中应力波的传播特性和层裂破坏模式。通过参数分析，研究了滤波单元的材料和几何属性对其储能效果的影响。研究结果表明：滤波单元有效降低了混凝土基体中应力波的传播速度和应力峰值；滤波单元的储能机制有效降低了混凝土基体中的能量；金属球的质量越大，滤波单元的储能效果越好，但弹性层的弹性模量和厚度需要通过适当分析进行设计以实现滤波单元的储能最大化；滤波混凝土基体的局部损伤耗散了荷载中的大量能量，有效降低了结构自由面附近的破坏程度。Abstract: Based on the working mechanism of local resonance materials, a filter concrete with stress wave attenuation characteristics is designed by embedding metal balls wrapped with elastic layer (filter units) in the concrete matrix. First, the stress wave attenuation mechanism of filter concrete is analyzed by simplifying the filter concrete structure into a mass-spring mechanical system. Then, the propagation velocity and peak stress of stress wave in normal concrete model and filter concrete model under impact load are compared by using numerical simulation approach. Through parameter analysis, the influence of the density of metal ball, elastic modulus and thickness of elastic layer on the energy storage of filter units are studied. Finally, the spalling damage patterns of normal concrete model and filter concrete model under impact load are compared. The results show that the filter units can effectively reduce the stress wave propagation velocity and magnitude of peak stress in the concrete matrix. The vibration of the metal balls and the deformation of the elastic layer form a good energy storage mechanism for filter units and effectively reduce the energy exerted by the impact load on the concrete matrix. The larger the mass of the metal balls, the better the energy storage effect of the filter units, while the elastic modulus and thickness of the elastic layer need to be designed through a proper analysis to maximize the energy storage of the filter units. The concrete matrix around the elastic layer has obvious stress concentration and local damage may occur, but the local damage of the filter concrete matrix dissipates a large amount of energy produced by the load, effectively reducing the degree of destruction near the free surface of the structure. Combined with the attenuation effect of the filter units on the stress wave, the filter concrete has achieved good impact resistance.
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Key words:
- filter concrete /
- local resonance /
- spalling damage /
- stress wave /
- energy storage mechanism
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图 8 数值模拟与实验条件下混凝土的应变时程曲线
Figure 8. Strain time history curves of concrete under numerical simulation and experiment
图 9 实验与数值模拟条件下的破坏形态对比
Figure 9. Comparison of failure patterns under experiment and numerical simulation
图 12 峰值为10 MPa冲击荷载下截面S1～S5的平均应力时程曲线
Figure 12. Average stress time history curves of sections S1–S5 under impact load with the peak value of 10 MPa
图 13 模型在0.140 ms时的纵截面应力云图
Figure 13. Stress contours of the model in the longitudinal section at 0.140 ms
图 14 模型在0.270 ms时的纵截面应力云图
Figure 14. Stress contours of the model in the longitudinal section at 0.270 ms
图 16 滤波混凝土模型中各部分的能量时程曲线
Figure 16. Energy time history curve of each part in the filter concrete model
图 17 滤波混凝土模型截面S0处单元E3～E5的应力时程曲线
Figure 17. Stress time history curves of elements E3–E5 at section S0 in the filter concrete model
图 18 金属球密度不同时混凝土基体的能量占比时程曲线
Figure 18. Energy proportion time history curves of concrete matrix with different metal ball densities
图 19 金属球密度不同时截面S4处的平均应力时程曲线
Figure 19. Average stress time history curves of section S4 with different metal ball densities
图 20 弹性层的弹性模量不同时混凝土基体的能量占比时程曲线
Figure 20. Energy proportion time history curves of concrete matrix with different elastic modulus of elastic layer
图 21 弹性层的弹性模量不同时单元E1与E2的位移时程曲线
Figure 21. Displacement time history curves of elements E1 and E2 with different elastic modulis of elastic layers
图 22 弹性层的厚度不同时混凝土基体的能量占比时程曲线
Figure 22. Energy proportion time history of concrete matrix with different thicknesses of elastic layers
图 23 无弹性包裹层时滤波混凝土模型中单元E1与E2的位移时程曲线
Figure 23. Displacement time history curves of elements E1 and E2 without an elastic layer in the model
图 24 具有不同厚度弹性层的滤波混凝土模型在0.120 ms时的纵截面应力云图
Figure 24. Stress contours in the longitudinal sections of the models with different thicknesses of elastic layers at 0.120 ms
图 28 峰值为40 MPa的冲击荷载作用下各模型截面S1～S4的平均应力时程曲线
Figure 28. Average stress time history curves of sections S1–S4 of different concrete models under impact load with the peak value of 40 MPa
表 1 混凝土的材料参数
Table 1. Material parameters of concrete
ρ/（kg·m−3） σc/MPa σt/MPa E/GPa μ a0y/MPa a1y 2 440 34 2.7 30 0.156 8.93 0.625 a2y/MPa−1 a0/MPa a1 a2/MPa−1 a1f a2f/MPa−1 6.437×10−3 11.82 0.446 2.02×10−3 0.442 2.957×10−3 
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表 2 滤波单元的材料参数
Table 2. Material parameters of a filter unit
材料 ρ/(kg·m−3) E/GPa μ 铅 11400 160 0.44 天然橡胶 900 0.047 0.42
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表 3 滤波混凝土模型的几何参数
Table 3. Geometric parameters of the filter concrete model
L/mm D/mm l/mm r/mm T/mm 500 74 75 22 2
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