Mesoscale numerical simulation on dynamical response of concrete slabs to explosion loading
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摘要: 考虑到一些对裂纹要求较严格的混凝土结构可能遭受到冲击载荷的威胁，利用混凝土三维细观力学模型对混凝土板在炸药爆炸（接触爆炸、封闭爆炸）载荷作用下的响应和破坏情况进行数值模拟，并就影响靶板内裂纹扩展结果的因素展开参数讨论。模型考虑了混凝土材料的内部细观结构（包括粗骨料体积分数、尺寸、级配等）以及三相材料力学性能的影响，准确地预测了混凝土板在2种爆炸条件下的裂纹形貌和开坑尺寸。通过与宏观均质模型的模拟结果进行对比可知，细观模型预测的接触爆炸条件下混凝土靶板的开坑形态、尺寸，以及封闭爆炸条件下混凝土盖板的主裂纹数量，均与实验观察更为贴近。此外，参数研究结果表明，三维细观力学模型的全局网格尺寸以及模型内各组分的相对网格尺寸均会对模拟结果的精度产生影响，选择与空气网格尺寸相当的混凝土网格尺寸，可以在获得较准确模拟结果的同时保证计算效率；骨料粒径大小也会影响混凝土板在爆炸载荷作用下的响应和破坏结果。混凝土三维细观力学模型能够反映混凝土结构在冲击载荷作用下的损伤和破坏的细观机理及影响因素，对指导工程设计和结构安全评估具有重要的理论意义和实际应用价值。Abstract: In order to study the damage of concrete structures which have relatively strict requirements on the formation and propagation of cracks, such as dam, pier and nuclear power plant containment, suffered by impact loads, numerical studies were conducted on the mechanical response of (reinforced) concrete slabs under two types of explosion loadings (contact explosion and closed explosion) by a three-dimensional meso-mechanical model together with a comprehensive computational dynamic constitutive model for concrete material, followed by a parametric discussion about the interfering factors of final crack morphologies in concrete targets. To generate the three-dimensional meso-mechanical model, regular hexahedral meshes were firstly applied to whole concrete specimens/structures and all the elements were assigned as mortar matrix, then the assemblies of elements as aggregate were randomly selected and the outer surfaces of each aggregate element assemblies were covered with shell elements as interfacial transition zone layers. The three-dimensional meso-mechanical model, in which taking the influence of internal meso-structures of concrete (e.g. volume fraction, size and gradation of coarse aggregate) and mechanical properties of three phase materials into consideration, succeeds in accurately predicting the crack patterns and crater sizes in the concrete slabs subjected to the two types of explosion loadings. It is shown that the numerical results are in good agreement with the experimental observations in terms of crater shapes and sizes in the contact explosion, as well as the number of main cracks in the closed explosion when compared with the predictions by the macroscopic homogeneous models. Parametric studies performed for further study on the influence factors of the explosion results indicate that both the global mesh size of the model and the relative mesh size of each component in the model produce effects on the accuracy of the numerical results, the balance between the computational accuracy and efficiency can be achieved by setting a similar mesh size for concrete material with air grids. In addition, the influence of the aggregate size can not be neglected in the response and failure of the concrete slabs subjected to explosion loadings. The three-dimensional meso-mechanical model plays an important role in understanding the meso-mechanism and influencing factors of the response and failure of the concrete structures subjected to impact loadings, which is of great theoretical and practical significance for engineering design and safety assessment.
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Key words:
- concrete /
- meso-mechanical model /
- explosion loading /
- crack morphology /
- crater size /
- grid sensitivity
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图 3 压缩强度为 47.2 MPa的混凝土靶板1/4有限元模型（未显示空气网格）
Figure 3. A one-fourth finite element model of the concrete slab with the compressive strength of 47.2 MPa (without air mesh )
图 4 接触爆炸作用下混凝土靶板破坏形貌的模拟结果与实验照片对比
Figure 4. Comparison of the numerically predicted cross-sectional views of the final crack patterns with the experimental observations in the concrete slab subjected to contact explosion
图 6 不同相对网格尺寸模型预测的混凝土靶板在接触爆炸作用下的破坏形貌
Figure 6. Comparison of the numerically predicted cross-sectional views of the final crack patterns by the meso-mechanical models with different relative mesh sizes
图 7 压缩强度为35 MPa的钢筋混凝土靶板及封闭容器1/4有限元模型（未显示空气网格）
Figure 7. A one-fourth finite element model for the reinforced concrete slab with the compressive strength of 35 MPa and the closed container (without air mesh)
图 8 封闭爆炸作用下钢筋混凝土盖板破坏形貌的模拟结果与实验照片对比
Figure 8. Comparison of the numerically predicted final crack patterns with the experimental observations on the upper surface of the reinforced concrete slab subjected to closed explosion
图 9 不同网格尺寸模型预测的钢筋混凝土盖板在封闭爆炸作用下的破坏形貌
Figure 9. Comparison of the numerically predicted final crack patterns on the upper surface of the reinforced concrete slab by the meso-mechanical models with different mesh sizes
图 10 不同相对网格尺寸模型预测的钢筋混凝土盖板的破坏形貌
Figure 10. Comparison of the numerically predicted final crack patterns on the upper surface of the reinforced concrete slab by the meso-mechanical models with different relative mesh sizes
图 11 不同骨料粒径范围的钢筋混凝土靶板在封闭爆炸作用下的破坏形貌
Figure 11. Comparison of the numerically predicted final crack patterns on the upper surface of the reinforced concrete slab by the meso-mechanical models with different aggregate sizes
表 1 砂浆基体、ITZ层及粗骨料材料参数
Table 1. Values of various parameters for mortar matrix, ITZ layer and coarse aggregate
材料 ${\rho _0}$/(kg·m−3) ${\rho _{{\text{s}}0}}$/(kg·m−3) ${p_{{\text{crush}}}}$/MPa ${p_{{\text{lock}}}}$/GPa K1/GPa K2/GPa K3/GPa 砂浆基体 2290 2680 10.2 3 14 30 10 ITZ层 1800 2680 6.1 3 12.6 30 10 粗骨料 2660 2680 29.3 3 19.1 −3000 150000 材料 n G/GPa ${f'_{\text{c}}}$/MPa ${f_{\text{t}}}$/MPa B N 砂浆基体 3 10.5 30.7 3.07 1.43 0.58 ITZ层 3 5.8 18.4 1.84 1.43 0.58 粗骨料 3 16.2 88 8.8 1.95 0.76 
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表 2 砂浆基体、ITZ层、粗骨料及混凝土材料参数
Table 2. Material parameters for mortar matrix, ITZ layer, coarse aggregate and concrete
材料 ${\rho _0}$/(kg·m−3) ${\rho _{{\text{s}}0}}$/(kg·m−3) ${p_{{\text{crush}}}}$/MPa ${p_{{\text{lock}}}}$/GPa K1/GPa K2/GPa K3/GPa 砂浆基体 2070 2680 6.1 3 11.7 30 10 ITZ层 1800 2680 3.6 3 10.5 30 10 粗骨料 2660 2680 29.3 3 19.1 −3000 150000 凝凝土 2314 2680 11.7 3 16.7 30 10 材料 n G/GPa ${f'_{\text{c}}}$/MPa ${f_{\text{t}}}$/MPa B N 砂浆基体 3 8.7 18.2 1.82 1.82 0.51 ITZ层 3 4.8 10.9 1.09 1.82 0.51 粗骨料 3 16.2 88 8.8 1.95 0.76 凝凝土 3 11 35 3.2 1.82 0.51
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