Seismic Damage Model of RC Pier Repaired with CFRP Considering Initial Damage
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摘要:
为研究碳纤维材料(CFRP)修复损伤钢筋混凝土(RC)结构遭受地震作用的损伤演化规律,准确量化修复损伤结构状态,进行了10个钢筋混凝土圆墩柱拟静力试验,其中,8个墩柱试件为使用不同CFRP加固方法进行修复的损伤试件. 基于试验结果,对8个典型地震损伤模型进行研究分析,引入材料性能折减系数来考虑结构初始损伤,建立了CFRP修复RC墩柱的双参数地震损伤模型,并根据试验现象和改进的损伤模型对钢筋混凝土结构的损伤程度进行量化分析. 研究表明:使用典型地震损伤模型计算修复柱的损伤指标时,计算试件破坏时的损伤指标普遍偏大,且同一墩柱模型损伤指数的变化趋势有较大差异,损伤指数发展趋势与试验现象不符;根据试件参数进行非线性回归分析,得到了组合系数与设计参数的经验表达式,建议的损伤模型能够较好模拟CFRP修复加固墩柱的地震损伤演化过程;定义了钢筋混凝土结构损伤的5个等级,并给出5个等级的损伤指标界限值;对中等损伤($0.3 < D \leqslant 0.6$,
D 为损伤指标)的墩柱结构,建议对结构表面修复平整后使用预应力CFRP加固以达到更好的效果.-
关键词:
- 地震损伤模型 /
- 损伤钢筋混凝土圆墩柱 /
- CFRP /
- 加固方法 /
- 修复
Abstract:In order to study the damage evolution law of damaged reinforced concrete (RC) structures repaired with carbon fiber reinforced plastics (CFRP) under earthquake action and accurately quantify the damage status of repaired structures, a quasi-static test of 10 circular RC piers was carried out, eight of which were repaired by different CFRP reinforcement methods. The test results were studied based on eight typical earthquake damage models, and a two-parameter seismic damage model for RC piers repaired with CFRP was established, in which the reduction coefficient of material properties was introduced to analyze the initial damage to the structure. The damage degree of RC structures was quantified according to the experimental phenomenon and the improved damage model. The results show that when the damage index of the repaired pier is calculated by using the typical earthquake damage model, the damage index of the damaged specimens is generally too large, and the variation of the damage index of the same pier model is quite different. The development trend of the damage index is not consistent with the experimental phenomenon. Based on the nonlinear regression analysis of the specimen parameters, the empirical expressions of the combination coefficients and design parameters are obtained. The proposed damage model can better simulate the seismic damage evolution process of piers repaired with CFRP. Five grades of RC structure damage are defined, and the damage index limit value of the five grades is given. For moderately damaged pier structures ($0.3 < D \leqslant 0.6$,
D is the damage index), it is recommended to use pre-stressed CFRP reinforcement after repairing and leveling the structural surface to achieve better results.-
Key words:
- seismic damage model /
- damaged circular RC pier /
- CFRP /
- reinforcement method /
- repair
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表 1 试件主要设计参数及结果
Table 1. Main design parameters and results of specimens
序号 试件编号 加固方式 设计参数 试验主要结果 损伤程度 d0/mm $ {t}_{\mathrm{f}} $/mm 预应力度 $ {P}_{\mathrm{m}\mathrm{a}\mathrm{x}} $/kN $ {k}_{\mathrm{h}} $ $\int \mathrm{d}E$/(kN·mm) 1 CC 无 0 0 0 0 34.69 18716.05 2 CC1C 普通 CFRP 0 0 0.167 0 37.31 0.28 27577.85 3 SC1C 普通 CFRP 0.1 0.1~0.5 0.167 0 36.61 0.26 26065.93 4 SC1P 预应力 CFRP 0.1 0.1~0.5 0.167 0.2 40.62 0.56 32374.62 5 MC1C 普通 CFRP 0.3 0.5~1.0 0.167 0 36.22 0.30 24803.49 6 MC1P 预应力 CFRP 0.3 0.5~1.0 0.334 0.2 40.22 0.48 30781.58 7 MC2P 预应力 CFRP 0.3 0.5~1.0 0.334 0.2 42.09 0.52 34563.85 8 BC1C 普通 CFRP 0.6 1.0~1.5 0.167 0 28.69 0.23 19941.42 9 BC1P 预应力 CFRP 0.6 1.0~1.5 0.167 0.2 35.45 0.44 25161.48 10 BC2P 预应力 CFRP 0.6 1.0~1.5 0.334 0.2 36.43 0.55 28356.57 表 2 单参数地震损伤模型
Table 2. Single-parameter seismic damage model
编号 研究者 模型表达式 D1 Powell 等[16] $ D_1 = {\left( {\dfrac{{{\delta _{\text{m}}} - {\delta _{\text{y}}}}}{{{\delta _{\text{u}}} - {\delta _{\text{y}}}}}} \right)^c} $ D2 Roufaiel 等[17] $ D_2 = \dfrac{{{k_{\text{f}}}\left( {{k_{\text{m}}} - {k_{\text{0}}}} \right)}}{{{k_{\text{m}}}\left( {{k_{\text{f}}} - {k_0}} \right)}} $ D3 Wang 等[18] $D_3=\dfrac{\mathrm{exp}(s\alpha )}{\mathrm{exp}(s)-1},\alpha =c\displaystyle\sum _{i=1}^{N}\dfrac{ {\delta }_{\text{m},i} }{ {\delta }_{\text{f} } }$ 表 3 双参数地震损伤模型
Table 3. Two-parameter seismic damage model
编号 研究者 模型表达式 D4 Park 等[11] $\begin{gathered} {\text{ } }D_4 = \dfrac{ { {\delta _{\text{m} } } }}{ { {\delta _{\text{u} } } }} + \beta \dfrac{ {\smallint {\text{d} }E} }{ { {F_{\text{y} } }{\delta _{\text{u} } } }}, \; \beta = \left( { - 0.447 + 0.073\lambda + 0.24{n_0} + 0.314{\rho _{\text{t} } } } \right) {0.7^{ {\rho _{\text{w} } } }}{\text{ } } \\ \end{gathered}$ D5 Chai 等[5] $\begin{gathered} D_5 = \dfrac{ { {\delta _{\text{m} } } }}{ { {\delta _{\text{u} } } }} + {\beta ^ * }\dfrac{ { {E_{} } } }{ { {F_{\text{y} } }{\delta _{\text{u} } } }}, \; \dfrac{ { {\beta ^*} } }{ { {\beta _{} } } } = \dfrac{ { {\mu _{\text{m} } } }}{ { {\mu _{\text{m} } } + \left( {1 - {\mu _{\text{m} } } } \right){\beta _{} } } }, \; {\mu _{\text{m} } } = {\delta _{\text{u} } }/{\delta _{\text{y} } } \\ \end{gathered}$ D6 王东升等[19] $ \begin{gathered} D_6 = (1 - \beta )\dfrac{{{\delta _{\text{m}}} - {\delta _{\text{y}}}}}{{{\delta _{\text{u}}} - {\delta _{\text{y}}}}} + \frac{{\beta \displaystyle\sum {{\beta_i}} {E_i}}}{{{F_{\text{y}}}\left( {{\delta _{\text{u}}} - {\delta _{\text{y}}}} \right)}},\quad{\delta _{\text{m}}} > {\delta _{\text{y}}}, {\text{ }}{\beta_i} = \left\{ {\begin{array}{*{20}{l}} {{\mathop \gamma \nolimits_{\rm{E}}},\quad{\text{ }}{\mu_i} \leqslant {\mu _0}}, \\ {{\mathop \gamma \nolimits_{\rm{E}}} + \dfrac{{{\mu_i} - {\mu _0}}}{{{\mu_{\rm{p}}} - {\mu _0}}}(1 - {\mathop \gamma \nolimits_{\rm{E}}}),\quad{\mu_i} > {\mu _0}} \end{array}} \right.\begin{array}{*{20}{c}} {{\text{ }}} \\ {{\text{ }}} \end{array} \\ \end{gathered} $ D7 付国等[20] $\begin{gathered} {\text{ } }D_7 = \dfrac{ { {\delta _{\text{m} } } }}{ { {\delta _{\text{u} } } }} + \dfrac{ {\displaystyle\sum { { {e} }_i}{ { {E} }_i} } }{ { {F_{\text{y} } }{\delta _{\text{u} } } }}, \; { { {e} }_i} = \dfrac{1}{ { { {\text{δ} }_{i{\text{m} } } }/{ { {\varDelta } }_{\text{y} } } }}{\log {\left( {\dfrac{ { {\delta _{\text{u} } } }}{ { { {{\varDelta } }_{\text{y} } } } } } \right)} }\left( {\dfrac{ { {\delta _{i{\text{m} } } } } }{ { { {{\varDelta } }_{\text{y} } } } } } \right) \\ \end{gathered}$ D8 傅剑平等[21] $ D_8 = {{\rm{e}}^{\left( {0.13{\mu _{\text{m}}} - 0.39} \right)}}\dfrac{{{\delta _{\text{m}}}}}{{{\delta _{\text{u}}}}} + {{\rm{e}}^{\left( {3.35 - 0.18{\mu _{\text{m}}}} \right)}}\dfrac{{\beta \smallint {\text{d}}E}}{{{F_{\text{y}}}{\delta _{\text{u}}}}} $ 表 4 试件破坏时损伤指标均值
Table 4. Mean value of damage index during specimen damage
编号 所有试件破坏时均值 对比柱 SC MC BC 修复试件均值 D1 0.48 0.47 0.86 0.75 0.75 0.79 D2 0.67 0.63 1.40 1.06 1.31 1.25 D3 1.30 1.24 2.56 2.05 2.10 2.24 D4 1.40 1.33 2.91 2.39 2.73 2.67 D5 1.77 1.71 3.73 3.06 3.47 3.42 D6 0.77 0.63 1.76 1.36 1.78 1.63 D7 0.87 0.98 1.86 1.58 1.58 1.67 D8 1.35 1.01 2.65 2.14 3.02 2.60 表 5 损伤试件材料性能退化系数
Table 5. Degradation coefficient of material property of damaged specimens
试件名称 Park 损伤指数 $ {\alpha }_{\rm{F}} $ SC1C 0.1 0.95 SC1P 0.1 0.95 MC1C 0.3 0.86 MC1P 0.3 0.86 MC2P 0.3 0.86 BC1C 0.6 0.73 BC1P 0.6 0.73 BC2P 0.6 0.73 表 6 损伤模型组合系数
Table 6. Combination coefficient of damage model
试件编号 $\varepsilon $ 能量项比例/% 位移项比例/% CC 0.037 55 45 CC1C 0.027 48 52 SC1C 0.025 45 55 SC1P 0.024 44 56 MC1C 0.023 44 56 MC1P 0.021 41 59 MC2P 0.019 38 62 BC1C 0.020 40 60 BC1P 0.021 40 60 BC2P 0.022 42 58 表 7 损伤指标量化
Table 7. Quantification of damage index
损伤程度 损伤量 损伤状态 具体描述 基本完好 $ 0\leqslant D\leqslant 0.100 $ 未损伤 柱侧向变形不明显,混凝土未开裂或少量裂缝且裂缝宽度小于 0.1 mm,CFRP 平整完好,结构处于弹性阶段,此阶段使用普通 CFRP 修复试件,性能便可得到恢复甚至一定程度增强 轻微破坏 $ 0.100 < D\leqslant 0.300 $ 轻度损伤 柱身有一定数量水平裂缝,裂缝宽度小于 0.5 mm,柱底部混凝土开裂,CFRP 较平整,使用普通 CFRP 或预应力 CFRP 修复结构都可以得到较好效果 中度破坏 $ 0.300 < D\leqslant 0.600 $ 可修复 柱脚出现细微斜裂缝,裂缝宽度小于 1.0 mm,柱底水平裂缝一定程度开展,应该对已有裂缝进行处理后外包 CFRP 修复,此阶段建议使用预应力 CFRP 进行修复,对于重要结构预应力 CFRP 加固可作为应急修复方法 严重破坏 $ 0.600 < D\leqslant 0.900 $ 不可修复 试件在此阶段承载力急速下降,刚度退化严重,CFRP 鼓曲变形,纵筋屈曲,有效约束面积急剧减小 倒塌 $ 0.900 < D\leqslant 1.00 $ 结构失效 纵筋屈曲、断裂,混凝土压溃,结构完全失效 -
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