设计基准期内地震活动区域既有结构寿命模型

高珺; 姚继涛; 程正杰

doi:10.6052/j.issn.1000-4750.2022.02.0160

设计基准期内地震活动区域既有结构寿命模型

高珺^{1, 2,},
姚继涛^{1, 2, ,},
程正杰^{1, 2,}

1.
西安建筑科技大学土木工程学院，陕西，西安 710055
2.
西安建筑科技大学结构工程与抗震教育部重点实验室，陕西，西安 710055

基金项目: 国家自然科学基金项目(51278401)

详细信息

作者简介:
高　珺(1991−)，女，甘肃天水人，博士，主要从事混凝土框架结构抗震可靠度研究(E-mail: gjtianshui@163.com)

程正杰(1995−)，男，甘肃天水人，博士生，主要从事钢筋混凝土结构可靠度研究(E-mail: chengzhengjie_1995@163.com)

通讯作者:
姚继涛(1963−)，男，陕西白水人，教授，博士，博导，主要从事可靠度研究(E-mail: yaojitao1224@163.com)

中图分类号: TU375.4
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出版历程
- 收稿日期: 2022-02-18
- 修回日期: 2022-04-27
- 网络出版日期: 2022-05-11
- 刊出日期: 2023-12-24

LIFETIME MODEL FOR EXISTING STRUCTURES DURING DESIGN REFERENCE PERIOD OF EARTHQUAKE ACTIVITY AREA

GAO Jun^{1, 2,},
YAO Ji-tao^{1, 2, ,},
CHENG Zheng-jie^{1, 2,}

1.
School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, China
2.
Key Lab of Structural Engineering and Earthquake Resistance, Ministry of Education, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, China

摘要

摘要:
在时变条件下，考虑结构的累积损伤是风险决策的关键点，对结构性能评估及寿命估算有重要意义。但是，结构累积损伤的计算通常涉及复杂的数学运算。基于此，该文的主要目的是在地震高发区，提出一种简化的估算结构寿命分布的模型。该模型假设给定结构的累积损伤仅由设计基准期内可能发生的一系列地震作用产生，此方法的优点在于可以通过简单的数学运算实现结构寿命估算。对所提出的简化结构寿命模型进行实例应用，以验证该方法的可行性。
- 钢筋混凝土框架 /
- 累积损伤 /
- 地震序列 /
- 结构寿命 /
- 可靠性
Abstract:
Under time-varying conditions, the key points of risk decision-making are important for structural performance assessment and lifetime estimation when considering structural accumulation damage. However, the calculation of structural cumulative damage is usually involved in complex mathematical operations. Based on this, the main purpose of this paper is to propose a simplified model for estimating the structural lifetime distribution in the seismic high-incidence region. The model assumes that the cumulative damage of an existing structure is only caused by a series of earthquake actions that may occur during the design reference period. And the advantage of this method is that the structural life can be estimated by simple mathematical operation. An example application is performed on the proposed simplified structural lifetime model to verify the feasibility of the method.
- reinforced concrete frame /
- cumulative damage /
- seismic sequence /
- structural lifetime /
- reliability

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图 1 损伤构件的建模和修改参数示例

Figure 1. Modeling and modification parameter example of injury components

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图 2 RC框架结构平面 /mm

Figure 2. RC frame structure plan

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图 3 材料本构模型

Figure 3. Constitutive model of materials

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图 4 结构响应均值的累积损伤概率分布函数

Figure 4. Cumulative damage probability distribution function of the structure response average value

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图 5 结构失效概率

Figure 5. Structural failure probability

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图 6 结构生存曲线

Figure 6. Structure survival curve

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表 1 西北地区各震源地震次数

Table 1 Number of earthquakes from each source in the northwest

震源号	震中烈度/级						总次数/次	统计年数/年
震源号	5.5~6.4	6.5~7.4	7.5~8.4	8.5~9.4	9.5~10.4	10.5~11.0	总次数/次	统计年数/年
西北1	17	5	1	1	1	1	26	50
西北2	6	4	1	0	0	0	11	50
西北3	7	4	1	1	0	0	13	50
西北背景	20	11	4	1	1	0	37	50

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表 2 损伤状态界限

Table 2 Damage state limit

性能状态	最大层间位移角 ${\theta _{\max }}$ /(%)^[21]	顶点最大位移 ${\delta _{\max }}$ /mm^[22]
轻微破坏	0.18	43.8
中等破坏	1.00	109.5
严重破坏	2.00	328.5
完全破坏	4.00	547.5

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以 ${\theta _{\max }}$ 为评估指标的累积生存率计算

Cumulative survival rate calculated by ${\theta _{\max }}$ as an evaluation index

第t_i次地震作用t_i	结构未出现损伤的地震数量n_i/次	结构出现损伤的地震数量d_i	结构累积生存率 $S({t_i})$ /(%)
${t_0}$	195	−	$S({t_0}) = 1$
${t_1}$	194	1	$S({t_1}) = S({t_0})\left(1 - \dfrac{1}{{194}}\right) = 0.995$
${t_2}$	190	4	$S({t_2}) = S({t_1})\left(1 - \dfrac{4}{{190}}\right) = 0.974$
${t_3}$	185	5	$S({t_3}) = S({t_2})\left(1 - \dfrac{5}{{185}}\right) = 0.948$
${t_4}$	179	6	$S({t_4}) = S({t_3})\left(1 - \dfrac{6}{{179}}\right) = 0.916$
${t_5}$	172	7	$S({t_5}) = S({t_4})\left(1 - \dfrac{7}{{172}}\right) = 0.879$
${t_6}$	161	11	$S({t_6}) = S({t_5})\left(1 - \dfrac{{11}}{{161}}\right) = 0.819$
${t_7}$	148	13	$S({t_7}) = S({t_6})\left(1 - \dfrac{{13}}{{148}}\right) = 0.747$
${t_8}$	133	15	$S({t_8}) = S({t_7})\left(1 - \dfrac{{15}}{{133}}\right) = 0.662$
${t_9}$	118	15	$S({t_9}) = S({t_8})\left(1 - \dfrac{{15}}{{118}}\right) = 0.578$
${t_{10}}$	103	15	$S({t_{10}}) = S({t_9})\left(1 - \dfrac{{15}}{{103}}\right) = 0.494$
${t_{11}}$	88	15	$S({t_{11}}) = S({t_{10}})\left(1 - \dfrac{{15}}{{88}}\right) = 0.410$
${t_{12}}$	73	15	$S({t_{12}}) = S({t_{11}})\left(1 - \dfrac{{15}}{{73}}\right) = 0.326$
${t_{13}}$	58	15	$S({t_{13}}) = S({t_{12}})\left(1 - \dfrac{{15}}{{58}}\right) = 0.241$

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以 ${\delta _{\max }}$ 为评估指标的累积生存率计算

Cumulative survival rate calculated by ${\delta _{\max }}$ as an evaluation index

第t_i次地震作用t_i	结构未出现损伤的地震数量n_i/次	结构出现损伤的地震数量d_i	结构累积生存率 $S({t_i})$ /(%)
${t_0}$	195	−	$S({t_0}) = 1$
${t_1}$	195	−	$S({t_1}) = 1$
${t_2}$	195	−	$S({t_2}) = 1$
${t_3}$	195	−	$S({t_3}) = 1$
${t_4}$	195	−	$S({t_4}) = 1$
${t_5}$	194	1	$S({t_5}) = S({t_4})\left(1 - \dfrac{1}{{194}}\right) = 0.995$
${t_6}$	187	7	$S({t_6}) = S({t_5})\left(1 - \dfrac{7}{{187}}\right) = 0.958$
${t_7}$	179	8	$S({t_7}) = S({t_6})\left(1 - \dfrac{8}{{179}}\right) = 0.915$
${t_8}$	166	13	$S({t_8}) = S({t_7})\left(1 - \dfrac{{13}}{{166}}\right) = 0.843$
${t_9}$	152	14	$S({t_9}) = S({t_8})\left(1 - \dfrac{{14}}{{152}}\right) = 0.766$
${t_{10}}$	138	14	$S({t_{10}}) = S({t_9})\left(1 - \dfrac{{14}}{{138}}\right) = 0.688$
${t_{11}}$	123	15	$S({t_{11}}) = S({t_{10}})\left(1 - \dfrac{{15}}{{123}}\right) = 0.604$
${t_{12}}$	108	15	$S({t_{12}}) = S({t_{11}})\left(1 - \dfrac{{15}}{{108}}\right) = 0.520$
${t_{13}}$	93	15	$S({t_{13}}) = S({t_{12}})(1 - \dfrac{{15}}{{93}}) = 0.436$

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表 5 拟合参数

Table 5 Fitting parameters

拟合参数	最大层间位移角 ${\theta _{\max }}$ /(%)	顶点最大位移 ${\delta _{\max }}$ /mm
a	−0.81	0.14
b	57.35	43.44
c	2.41	4.43

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参考文献(22)

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CHENG Zheng-jie, chengzhengjie_1995@163.com

1.
School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, China
2.
Key Lab of Structural Engineering and Earthquake Resistance, Ministry of Education, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, China

设计基准期内地震活动区域既有结构寿命模型

作者简介: 高 珺(1991−)，女，甘肃天水人，博士，主要从事混凝土框架结构抗震可靠度研究(E-mail: gjtianshui@163.com) 程正杰(1995−)，男，甘肃天水人，博士生，主要从事钢筋混凝土结构可靠度研究(E-mail: chengzhengjie_1995@163.com)

通讯作者: 姚继涛(1963−)，男，陕西白水人，教授，博士，博导，主要从事可靠度研究(E-mail: yaojitao1224@163.com)

计量

出版历程

LIFETIME MODEL FOR EXISTING STRUCTURES DURING DESIGN REFERENCE PERIOD OF EARTHQUAKE ACTIVITY AREA

计量

出版历程

目录

CHENG Zheng-jie, chengzhengjie_1995@163.com

作者简介:
高　珺(1991−)，女，甘肃天水人，博士，主要从事混凝土框架结构抗震可靠度研究(E-mail: gjtianshui@163.com)

程正杰(1995−)，男，甘肃天水人，博士生，主要从事钢筋混凝土结构可靠度研究(E-mail: chengzhengjie_1995@163.com)

通讯作者:
姚继涛(1963−)，男，陕西白水人，教授，博士，博导，主要从事可靠度研究(E-mail: yaojitao1224@163.com)