Modified discrete numerical model for reinforced concrete structures
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摘要: 提出一种考虑粘结滑移效应的钢筋混凝土改进型分离式数值模型。在混合物理论基础上，该模型兼顾混凝土基体和钢筋的力学行为，且基于钢筋混凝土界面粘结滑移模型，获得了钢筋等效模型。改进型分离式数值模型由于对钢筋及其界面无显式离散要求，使得钢筋的运用完全独立于其几何形状，同时对混凝土网格没有约束，并且不增加计算成本，因此该模型可适用于钢筋混凝土宏观结构层面分析。通过钢筋混凝土构件-结构的爆炸实验，对改进型分离式数值模型进行层次化验证。对比结果表明，考虑粘结滑移效应的有限元模型能够更好地预测钢筋混凝土结构的宏观力学行为。Abstract: The interaction between rebar and concrete must always be considered to well describe and predict the mechanical behavior of reinforced concrete (RC) structures. A common way to model RC structures is by discrete reinforcements in finite element models where the discrete reinforcements imply that bond conditions between rebar and concrete are perfect. In order to take into account the bond-slip phenomenon, a modified discrete numerical model for RC structures is presented in this paper. The model is formulated within the framework of the mixture theory, considering two phases corresponding to the matrix concrete and the reinforcement bars and incorporating bond-slip effects to the stress-strain relation of the latter by considering the bond-slip model recommended by CEB-FIB. A nonlinear equivalent stress-strain relation for discrete steel bars is generated by incorporating the bond-slip strain to the strain of bars. Based on this model, a comprehensive parametric study is accomplished to obtain the influence of the parameters, including the strengths of the concrete and steel bars as well as the diameter of bars on the modified stress-strain relation of the discrete steel bars. In comparison to the traditional discrete numerical model where interface elements are generated via connecting the degrees of freedom of the bars and concrete meshing, the new model allows for the slipping of the steel bars without explicit discretization of the steel bars and the steel/concrete interfaces. This fact makes it attractive for numerical simulation of concrete structures at the macrostructural level. Using a code JUST-PANDA that is developed in-house, the model is verified by the explosion experiments at the component level and the structural level respectively. The comparisons with experimental results show that the new model can provide a more reliable prediction of the concrete structural behavior due to the consideration of the bond-slip effects in the stress-strain relation of the discrete steel bars by means of a simple procedure.
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Key words:
- concrete /
- reinforcement bar /
- bond-slip /
- explosion load
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图 1 钢筋混凝土框架结构分离式有限元模型
Figure 1. Improved discrete finite element model of reinforced concrete frame structures
图 3 弹性模量缩放因子
$E^{\rm {eq}}_{\rm f}/E_{\rm f}$ 与粘结区长度l的关系Figure 3. Relationship between the scaling factor of the elastic modulus (
$E^{\rm {eq}}_{\rm f}/E_{\rm f}$ ) and the length of the bonding zone (l) under different physical parameters
图 4 塑性硬化模量缩放因子
$H^{\rm {eq}}_{\rm f}/H_{\rm f}$ 与粘结区长度l的关系Figure 4. Relationship between the scaling factor of the plastic hardening modulus (
$H^{\rm {eq}}_{\rm f}/H_{\rm f}$ ) and the length of the bonding zone (l) under different physical parameters
图 6 柱竖向位移时程曲线及破坏形貌对比
Figure 6. Comparison of the vertical displacement-time history curves and failure morphology of columns
图 7 板竖向位移时程曲线对比
Figure 7. Comparison of the vertical displacement-time history curves of the slab
图 8 网格尺寸对板跨中竖向位移时程曲线的影响
Figure 8. Effect of mesh size on the vertical displacement-time history curves of the slab
图 9 改进型分离式数值有限元模型及实验（单位：m）
Figure 9. Improved discrete finite element model and experiment (Unit: m)
图 10 框架结构破坏形貌对比
Figure 10. Comparison of the failure morphology of the frame structure
图 11 低层中柱位移时程曲线对比
Figure 11. Comparison of the displacement-time history curves of the lower mid column
表 1 钢筋等效材料参数
Table 1. Equivalent material parameters of rebar
钢筋 $ f_{\text{y}}^{{\text{eq}}} $/MPa $ E_{\text{f}}^{{\text{eq}}} $/GPa $ H_{\text{f}}^{{\text{eq}}} $/MPa Vf/% 纵筋 425.0 162.2 788.8 78.5 箍筋 368.1 150.2 656.5 50.0 
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