考虑结构损伤的CFRP修复RC墩柱地震损伤模型研究

龚婉婷; 钱永久; 徐望喜

doi:10.3969/j.issn.0258-2724.20220176

考虑结构损伤的CFRP修复RC墩柱地震损伤模型研究

doi: 10.3969/j.issn.0258-2724.20220176

西南交通大学土木工程学院，四川成都 610031

基金项目: 国家自然科学基金（51778532）

详细信息

作者简介:
龚婉婷（1993—），女，博士研究生，研究方向为桥梁抗震与加固，E-mail：wanting@my.swjtu.edu.cn

通讯作者:
钱永久（1963—），男，教授，博士生导师，研究方向为桥梁检测与加固， E-mail：yjqian@sina.com

中图分类号: TU375.3；U445.7.2
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出版历程
- 收稿日期: 2022-03-08
- 修回日期: 2022-06-11
- 网络出版日期: 2023-09-18
- 刊出日期: 2022-07-07

Seismic Damage Model of RC Pier Repaired with CFRP Considering Initial Damage

School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China

摘要

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.
- 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.
- seismic damage model /
- damaged circular RC pier /
- CFRP /
- reinforcement method /
- repair

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图 1 试件构造详图

Figure 1. Structure of specimen

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图 2 加载制度及预损伤方案

Figure 2. Loading system and pre-damage scheme

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图 3 试件BCIP损伤过程描述

Figure 3. Damage evolution description of specimen BCIP

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图 4 部分试件滞回曲线

Figure 4. Hysteretic curves of some specimens

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图 5 损伤指数变化趋势

Figure 5. Variation of damage indices

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图 6 本文模型计算试件加载过程损伤指标

Figure 6. Damage index of specimens during loading by proposed model

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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
序号	试件编号	加固方式	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

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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]	$D_3=\dfrac{\mathrm{exp}(s\alpha )}{\mathrm{exp}(s)-1}，\alpha =c\displaystyle\sum _{i=1}^{N}\dfrac{ {\delta }_{\text{m},i} }{ {\delta }_{\text{f} } }$

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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}}}}} $

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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

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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

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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

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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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