Study on Failure Mode and Deformation Capacity of Reinforced Concrete Columns
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摘要: 对钢筋混凝土（RC）柱在地震作用下的变形性能进行量化，本文从太平洋地震研究中心柱数据库中收集到123根RC柱抗震性能试验数据，提出基于参数剪跨比和弯剪比的RC柱破坏形态判别标准；在弯曲破坏、弯剪破坏、剪切破坏三种破坏形态下，研究了轴压比、剪跨比、配箍特征值等参数对位移角的显著性影响，通过回归分析归纳出三种破坏形态下屈服位移角和极限位移角的回归方程，回归系数显著性概率均小于0.05。结果表明：本文提出的RC柱破坏形态判别标准准确度高，适应性强；位移角线性回归方程具有合理性。Abstract: In order to quantify the deformation performance and failure characteristics of RC columns under earthquake action, this paper collected 123 reinforced concrete (RC) column test data from PEER (Pacific Earthquake Research Center) database, and proposed the standard of RC column failure morphology based on parameter shear span ratio and bending-shear ratio. Under the three failure modes of bending failure, bending shear failure and shear failure, the significant effects of parameters such as axial compression ratio, shear span ratio, hoop characteristic value, volume hoop ratio, longitudinal reinforcement ratio on the displacement angle were studied. Through regression analysis, the regression equations of yield displacement angle and ultimate displacement angle under three failure modes were summarized and the significance probability of regression coefficient is less than 0.05. The results show that the criterion of RC column damage morphology proposed in this paper has high accuracy and strong adaptability; the linear regression equation of displacement angle is reasonable.
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Key words:
- RC frame column /
- Deformation limit /
- Damage form discrimination /
- Displacement angle
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图 2 破坏形态与${{{V_{\rm{p}}}} \mathord{\left/ {\vphantom {{{V_{\rm{p}}}} {({{{V_{\rm{n}}}} \mathord{\left/ {\vphantom {{{V_{\rm{n}}}} k}} \right. } k})}}} \right. } {({{{V_{\rm{n}}}} \mathord{\left/ {\vphantom {{{V_{\rm{n}}}} k}} \right. } k})}}$的关系
Figure 2. Relationship between failure form and $ {{{V_{\rm{p}}}} \mathord{\left/ {\vphantom {{{V_{\rm{p}}}} {({{{V_{\rm{n}}}} \mathord{\left/ {\vphantom {{{V_{\rm{n}}}} k}} \right. } k})}}} \right. } {({{{V_{\rm{n}}}} \mathord{\left/ {\vphantom {{{V_{\rm{n}}}} k}} \right. } k})}} $
图 3 破坏形态与弯剪比和剪跨比的关系
Figure 3. Relationship between Failure Mode and Bending-shear Ratio and Shear-to-span Ratio
表 1 ASCE/SEI 41-06标准中的柱破坏模式划分
Table 1. Column failure mode division in ASCE/SEI 41-06
折减后的弯剪比 柱中箍筋细部构造形式 135°弯钩的箍筋 90°弯钩的封闭环形箍 其他构造形式 ${V_\text{p}}/({V_\text{n}}/k) \leqslant 0.60$ 弯曲破坏 弯剪破坏 弯剪破坏 $0.60 < {V_\text{p}}/({V_\text{n}}/k) \leqslant 1$ 弯剪破坏 弯剪破坏 剪切破坏 ${V_\text{p}}/({V_\text{n}}/k) > 1$ 剪切破坏 剪切破坏 剪切破坏 
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表 2 破坏形态与剪跨比和配箍特征值、体积配箍率、配筋率之间的关系
Table 2. Relationship between failure mode and shear span ratio and hoop characteristic value, volume hoop ratio and reinforcement ratio
破坏状态 剪跨比$\lambda $ 配箍特征值${\beta _{v}}$ 体积配箍率${\rho _{v}}$% 配筋率$\rho $% 弯曲破坏 $1.50 \leqslant \lambda \leqslant 5.50$ $0.02 \leqslant {\beta _{v}} \leqslant 0.45$ $0.30 \leqslant \rho _{v}^{} \leqslant 2.80$ $0.70 \leqslant \rho \leqslant 3.30$ 弯剪破坏 $1.50 \leqslant \lambda \leqslant 3.22$ $0.02 \leqslant {\beta _{v}} \leqslant 0.23$ $0.20 \leqslant \rho _{v}^{} \leqslant 1.60$ $1.30 \leqslant \rho \leqslant 3.80$ 剪切破坏 $1 \leqslant \lambda \leqslant 3.22$ $0.02 \leqslant {\beta _{v}} \leqslant 0.51$ $0.20 \leqslant \rho _{v}^{} \leqslant 1.80$ $1.30 \leqslant \rho \leqslant 4.10$
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表 3 钢筋混凝土柱破坏形态判别标准
Table 3. Discrimination criteria for failure mode of reinforced concrete columns
破坏形态 判断标准 弯曲破坏 $2 < \lambda \leqslant 4$且${V_\text{p}}/({V_\text{n}}/k) \leqslant 0.7$ $\lambda > 4$且${V_\text{p}}/({V_\text{n}}/k) \leqslant 0.8$ 弯剪破坏 $\lambda \leqslant 2$且${V_\text{p}}/({V_\text{n}}/k) < 1.0$ $2 < \lambda \leqslant 4$且$0.7 < {V_\text{p}}/({V_\text{n}}/k) < 1.0$ 剪切破坏 $\lambda \leqslant 2$且${V_\text{p}}/({V_\text{n}}/k) \geqslant 1.0$ $2 < \lambda \leqslant 4$且${V_\text{p}}/({V_\text{n}}/k) \geqslant 1.0$
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表 4 各影响因素与屈服位移角的相关系数
Table 4. Correlation coefficients between various influencing factors and yield displacement angle
影响因素 弯曲破坏柱 弯剪破坏柱 剪切破坏柱 Spearman
相关系数Sig.（双侧） Spearman
相关系数Sig.（双侧） Spearman
相关系数Sig.（双侧） 轴压比 -.822** .000 -.925** .000 -.621* .031 轴压比倒数 .822** .000 .925** .000 .621* .031 剪跨比 .063 .647 .042 .857 .120 .726 配箍特征值 .187 .094 -.279 .167 .320 .227 体积配箍率 -.017 .903 -.270 .034 .381 .247 纵筋配筋率 .360** .007 .251 .237 -.506 .112 注：**在0.01显著性水平（双侧）上显著相关；*在0.05显著性水平（双侧）上显著相关
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表 5 各影响因素与极限位移角的相关系数
Table 5. Correlation coefficients between various influencing factors and ultimate displacement angle
影响因素 弯曲破坏柱 弯剪破坏柱 剪切破坏柱 Spearman
相关系数Sig.(双侧) Spearman
相关系数Sig.(双侧) Spearman
相关系数Sig.(双侧) 轴压比 -.773** .000 -.798** .000 -.922** .000 轴压比倒数 .773** .000 .798** .000 .922** .000 剪跨比 -.269* .037 .563** .010 .837** .000 配箍特征值 .458** .000 -.588** .006 .611 .108 体积配箍率 .348** .006 -.475* .034 .522 .184 纵筋配筋率 .509** .000 .181 .445 -.638 .015 注：**在0.01显著性水平（双侧）上显著相关；*在0.05显著性水平（双侧）上显著相关
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表 6 不同破坏形态下位移角的回归方程
Table 6. Regression equations of displacement angles under different failure modes
破坏状态 回归方程 弯曲破坏 ${\theta _{y}} = 0.011 - 0.015n + 0.136\rho $ ${\theta _{u}} = 0.170 - 0.062n + 0.030{\beta _{v}} + 1.744\rho $ 弯剪破坏 ${\theta _{y}} = 0.011 - 0.015n + 0.155\rho $ ${\theta _{u}} = 0.029 - 0.097n + 0.029\lambda + 0.020{\beta _{v}}$ 剪切破坏 ${\theta _{y}} = 0.032 - 0.012n + 0.745\rho $ ${\theta _{u}} = 0.005 - 0.030n + 0.012\lambda - 0.007\rho $
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表 7 不同破坏形态下位移角回归方程中的R，R2和Adjusted R2
Table 7. Correlation Coefficients R, R2 and Adjusted R2 in the Displacement Angle Regression Equation under Different Failure Modes
屈服位移角 极限位移角 弯曲破坏 弯剪破坏 剪切破坏 弯曲破坏 弯剪破坏 剪切破坏 R 0.872 0.876 0.885 0.892 0.894 0.994 R2 0.761 0.768 0.784 0.795 0.799 0.989 Adjusted R2 0.752 0.757 0.779 0.782 0.785 0.981
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