斜拉桥模块化功能恢复函数研究

段佳宏; 罗天; 尹伟涛; 张杨; 廖泺恒; 陈治宇; 赵灿晖

doi:10.3969/j.issn.0258-2724.20250204

斜拉桥模块化功能恢复函数研究

doi: 10.3969/j.issn.0258-2724.20250204

段佳宏^{1, 2,},
罗天²,
尹伟涛¹,
张杨²,
廖泺恒²,
陈治宇²,
赵灿晖^{1, 3, ,}

1.
西南交通大学土木工程学院，四川成都 610031
2.
四川省公路规划勘察设计研究院有限责任公司，四川成都 610041
3.
抗震安全与韧性四川省重点实验室，四川成都 610031

基金项目: 国家自然科学基金区域联合基金项目（U21A20154）

详细信息

作者简介:
段佳宏（1994—），男，工程师，博士，研究方向为桥梁抗震韧性，E-mail：djer_holmes@163.com

通讯作者:
赵灿晖（1970—），男，教授，博士，研究方向为桥梁抗震韧性，E-mail：zch2887@163.com

中图分类号: U448.27
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- 文章访问数: 12
- HTML全文浏览量: 7
- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2025-04-22
- 修回日期: 2025-10-12
- 网络出版日期: 2026-06-30

Research on Modular Functionality Recovery Functions for Cable-Stayed Bridges

1.
School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China
2.
Sichuan Highway Planning, Survey, Design and Research Institute Ltd., Chengdu 610041, China
3.
Sichuan Provincial Key Laboratory of Earthquake Safety and Resilience, Chengdu 610031, China

摘要

摘要:
为量化斜拉桥抗震韧性评价中的功能恢复权重系数，避免依赖经验或专家问卷的主观性，提出一种基于模块化功能恢复函数的抗震韧性评价方法. 首先，采用Pair Copula分层模型将斜拉桥划分为构件、子系统及系统3个层次，分别计算各层次的地震易损性；其次，基于各子系统在不同损伤状态下的概率比值，进行概率加权，构建功能恢复权重系数的量化模型；进而，综合考虑功能恢复、修复时间与修复路径，建立模块化功能恢复函数，并通过集成子系统修复顺序形成系统级功能恢复函数；最终，建立斜拉桥抗震韧性评价流程，并以某斜拉桥为例进行抗震韧性评价. 结果表明：功能恢复权重系数随地震动强度变化，与各子系统损伤程度密切相关；若采用常数型权重系数，支座子系统的恢复贡献将被低估约50%；斜拉桥各构件地震响应具有较强的相关性，若假设构件完全独立，系统易损性计算误差可达28%～53.3%；在规范规定的地震动强度范围内，忽略子系统修复顺序会使系统韧性指数低估约9%.
- 斜拉桥 /
- 抗震韧性 /
- 功能恢复函数 /
- 概率加权 /
- 修复顺序
Abstract:
To quantify the functionality recovery weighting coefficient in the seismic resilience assessment of cable-stayed bridges and avoid the subjectivity relying on experience or expert questionnaires, a seismic resilience assessment method based on a modular functionality recovery function was proposed. First, a Pair Copula hierarchical model was employed to divide a cable-stayed bridge into three levels, i.e., components, subsystems, and the system, and the seismic fragility of each level was calculated. Second, based on the probability ratio of each subsystem under different damage states, probability weighting was performed to construct a quantitative model of the functionality recovery weighting coefficient. Furthermore, a modular functionality recovery function was established by comprehensively considering functionality recovery, repair time, and repair path. Then, a system-level functionality recovery function was formed by integrating the repair sequence of subsystems. Finally, a seismic resilience assessment procedure for cable-stayed bridges was established, and a seismic resilience assessment was conducted taking a cable-stayed bridge as an example. The results indicate that the functionality recovery weighting coefficient varies with the ground motion intensity and is closely related to the damage degree of each subsystem. If a constant weighting coefficient is adopted, the recovery contribution of the bearing subsystem is underestimated by approximately 50%. The seismic responses of the components of cable-stayed bridges have strong correlations; if the components are assumed to be completely independent, the calculation error of the system fragility can reach 28%–53.3%. Within the ground motion intensity range specified by codes, if the repair sequence of subsystems is neglected, the system resilience index is underestimated by approximately 9%.
- cable-stayed bridge /
- seismic resilience /
- functionality recovery function /
- probability weighting /
- repair sequence

HTML全文

图 1 Pair Copula迭代示意

Figure 1. Schematic diagram of Pair Copula iteration

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图 2 子系统功能恢复函数模块

Figure 2. Subsystem functionality recovery function module

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图 3 斜拉桥系统功能恢复函数

Figure 3. System functionality recovery function of cable-stayed bridge

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图 4 韧性概念示意图

Figure 4. Schematic diagram of resilience concept

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图 5 基于斜拉桥模块化功能恢复函数的抗震韧性评价流程

Figure 5. Seismic resilience assessment procedure based on modular functionality recovery function for cable-stayed bridges

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图 6 斜拉桥非线性有限模型

Figure 6. Nonlinear finite element model diagram of cable-stayed bridge

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图 7 斜拉桥功能恢复函数

Figure 7. Functionality recovery function of cable-stayed bridge

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图 8 斜拉桥Pair Copula分层配对模型

Figure 8. Pair Copula hierarchical pairing model diagram of cable-stayed bridge

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图 9 子系统易损性曲线图

Figure 9. Subsystem fragility curves

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图 10 系统易损性曲线图

Figure 10. System fragility curves

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图 11 震后剩余功能函数

Figure 11. Post-earthquake residual functionality function

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图 12 功能恢复权重系数

Figure 12. Functionality recovery weighting coefficient

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图 13 功能恢复曲线

Figure 13. Functionality recovery curves

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图 14 韧性指数图

Figure 14. Resilience index diagram

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表 1 斜拉桥损伤状态与功能损失比对应关系表

Table 1. Correspondence between damage states and functionality loss ratios of cable-stayed bridges

损伤状态	L_j
轻微损伤	15%
中等损伤	30%
严重损伤	60%
完全破坏	100%

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表 2 斜拉桥不同损伤状态下修复时间分布表/天

Table 2. Repair time distribution of cable-stayed bridges under different damage states （d）

损伤程度	t_f		t_i		T_b
损伤程度	min	max	min	max	min	max
轻微损伤	5	120	5	30	3	8
中等损伤	15	170			3	8
严重损伤	55	220			5	10
完全破坏	75	270			5	10

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表 3 最优Copula函数及检验结果

Table 3. Optimal Copula function and test results

位置	构件名	Copula函数类型	参数1	参数2	KS检验统计量	p值
第1层	2#P	Frank	13.94	\	0.045	0.985
第1层	3#P	Frank	12.77	\	0.040	0.997
第2层	桥塔体系	Gaussian	0.99	\	0.040	0.997
	桥墩体系	Gumbel	3.42	\	0.090	0.377
	支座1	Gaussian	0.96	\	0.110	0.167
	支座2	Gumbel	6.22	\	0.105	0.208
第3层	塔-墩体系	t	0.91	8.36	0.065	0.779
第3层	支座体系	Gumbel	8.84	\	0.095	0.312
第4层	斜拉桥系统	Clayton	2.68	\	0.085	0.449

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