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浙江大学学报(工学版)
浙江大学学报(工学版)  2023, Vol. 57 Issue (6): 1080-1089    DOI: 10.3785/j.issn.1008-973X.2023.06.003
土木工程、水利工程     
脉冲型地震动作用下钢框架结构地震需求概率模型
赵国臣1(),徐龙军1,*(),杜佳俊2,朱敬洲2,朱兴吉2,谢礼立1
1. 江汉大学 精细爆破国家重点实验室，湖北 武汉 430056
2. 哈尔滨工业大学（威海） 海洋工程学院，山东 威海 264209
Probabilistic seismic demand models for steel frame structures subjected to pulse-like ground motions
Guo-chen ZHAO1(),Long-jun XU1,*(),Jia-jun DU2,Jing-zhou ZHU2,Xing-ji ZHU2,Li-li XIE1
1. State Key Laboratory of Precision Blasting, Jianghan University, Wuhan 430056, China
2. School of Ocean Engineering, Harbin Institute of Technology (Weihai), Weihai 264209, China
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摘要：

基于实际脉冲型地震动数据建立钢框架结构的Abaqus有限元模型，建立钢框架结构4种形式（最大底部剪力、最大底部弯矩、最大层间位移角和顶层位移）的地震需求概率模型. 为了方便模型应用和明确模型参数的物理意义，构建模型时在规范方法和力学原理计算结果的基础上增加修正项，基于贝叶斯方法进行模型优化和参数估计. 结果表明，所建立的4种地震需求概率模型能够获取有限元数值解的无偏估计. 以最大层间位移角概率模型为例，可以得到20层钢框架结构的地震易损性曲线. 相对于普通类型地震动作用，钢框架结构在脉冲型地震动作用下的失效概率显著偏大.
关键词： 地震需求概率模型;  钢框架结构;  脉冲型地震动;  非线性时程分析;  贝叶斯方法    
Abstract:

Finite element models of steel frame structures were built by a commercial finite element software Abaqus, and the simulated seismic responses of the steel frame structures to pulse-like ground motions were used as the data to develop probabilistic seismic demand models. Four types of seismic demands were considered, including the maximum bottom shear force, the maximum bottom moment, the maximum story drift, and the top displacement of steel frame structures, and each of them was represented by a separate probabilistic model. In order to facilitate the application of the model and make the model parameters have clear physical meaning, the probabilistic seismic demand models were obtained by adding correction terms to the results obtained by code-based methods and mechanics principles. The Bayesian method was used for model optimization and parameter estimation. Results show that the four probabilistic seismic demand models can obtain the unbiased estimation of the finite element numerical value. Using the maximum story drift probability model, the seismic fragility curve of a 20-story steel frame structure was obtained. The analysis shows that the failure probability of the steel frame structure to pulse-like ground motions is significantly higher than that of ordinary ground motions.
Key words: probability seismic demand model    steel frame structure    pulse-like ground motion    nonlinear time history analysis    Bayesian method
收稿日期: 2022-05-16 出版日期: 2023-06-30
CLC:  P 315.9  
基金资助: 国家自然科学基金资助项目（51908169，U2139207）；江汉大学学科特色专项项目资助（2022XKZX-ZC-01）
通讯作者: 徐龙军     E-mail: zgc011@126.com;xulongjun80@163.com
作者简介: 赵国臣（1990—），男，副教授，博士，从事地震工程研究. orcid.org/0000-0001-6995-2761. E-mail： zgc011@126.com
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引用本文:

赵国臣,徐龙军,杜佳俊,朱敬洲,朱兴吉,谢礼立. 脉冲型地震动作用下钢框架结构地震需求概率模型[J]. 浙江大学学报(工学版), 2023, 57(6): 1080-1089.

Guo-chen ZHAO,Long-jun XU,Jia-jun DU,Jing-zhou ZHU,Xing-ji ZHU,Li-li XIE. Probabilistic seismic demand models for steel frame structures subjected to pulse-like ground motions. Journal of ZheJiang University (Engineering Science), 2023, 57(6): 1080-1089.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2023.06.003    或    https://www.zjujournals.com/eng/CN/Y2023/V57/I6/1080

图 1  不同方法获取的最大底部剪力结果比较
分析步 $ {\theta _{{_{V1}}}} $ $ {\theta _{{_{V2}}}} $ $ {\theta _{{_{V3}}}} $ $ {\theta _{{_{V4}}}} $ $ {\theta _{{_{V5}}}} $ $ {\theta _{{_{V6}}}} $ $ {\theta _{{_{V7}}}} $ $ {\theta _{{_{V8}}}} $ $ {\theta _{{_{V9}}}} $ $ {\theta _{{_{V10}}}} $ $\mu{(\sigma _{ {_V} }) }$
1 0.179 0.092 0.916 0.721 0.638 0.315 0.524 0.519 0.554 0.066 0.127
2 0.139 0.092 — 0.650 0.781 0.279 0.460 0.465 0.537 0.068 0.128
3 0.124 0.093 — 0.613 — 0.236 0.311 0.238 0.427 0.067 0.128
4 0.057 0.093 — — — 0.274 0.289 0.212 0.449 0.068 0.130
5 0.056 0.095 — — — 0.351 0.329 0.224 — 0.070 0.133
6 0.059 0.104 — — — — 0.129 0.110 — 0.072 0.136
7 0.076 0.100 — — — — — 0.245 — 0.050 0.165
表 1  最大底部剪力概率模型优化过程各参数变异系数和模型标准差均值
参数 μ σ ρ
$ {\theta _{_{{V2}}}} $ $ {\theta _{_{{V7}}}} $ $ {\theta _{_{{V10}}}} $ $ {\sigma _{{_V}}} $
$ {\theta _{_{{V2}}}} $ ?0.023 2 0.002 4 1.00 — — —
$ {\theta _{_{{V7}}}} $ ?0.003 9 0.000 5 ?0.26 1.00 — —
$ {\theta _{_{{V10}}}} $ ?0.144 8 0.010 4 0.42 ?0.64 1.000 —
${\sigma _{{_V} } }$ 0.136 1 0.008 6 ?0.02 0.01 ?0.004 1.0
表 2  最大底部剪力概率模型参数的后验分布信息
图 2  不同方法获取的最大底部弯矩结果比较
参数 μ σ ρ
$ {\theta _{_{{M2}}}} $ $ {\theta _{_{{M10}}}} $ $ {\sigma _{_{{M}}}} $
$ {\theta _{_{{M2}}}} $ ?0.0151 0.0032 1.000 — —
$ {\theta _{_{{M10}}}} $ 0.3426 0.0423 0.590 1.00 —
$ {\sigma _{_{{M}}}} $ 0.1626 0.0086 0.001 0.02 1.0
表 3  最大底部弯矩概率模型参数后验分布信息
图 3  不同方法获取的最大层间位移角结果比较
参数 μ σ ρ
$ {\theta _{{\delta} 2}} $ $ {\theta _{{\delta} 8}} $ $ {\theta _{{\delta} 10}} $ $ {\sigma _{{\delta} 10}} $
$ {\theta _{{\delta} 2}} $ 0.022 0.004 0 1.000 — — —
$ {\theta _{{\delta} 8}} $ 0.001 0.0003 ?0.130 1.000 00 — —
$ {\theta _{{\delta} 10}} $ ?0.079 0.012 0 0.310 ?0.420 00 1.00 —
$ {\sigma _{{\delta} 10}} $ 0.211 0.014 0 ?0.007 0.00005 ?0.02 1.0
表 4  最大层间位移角概率模型参数的后验分布信息
图 4  不同方法获取的顶层位移结果比较
参数 μ σ ρ
$ {\theta _{{d1}}} $ $ {\theta _{{d2}}} $ $ {\theta _{{d5}}} $ $ {\theta _{{d6}}} $ $ {\theta _{{d10}}} $ $ {\sigma _{{d}}} $
$ {\theta _{{d1}}} $ 0.808 0.081 1.00 — — — — —
$ {\theta _{{d2}}} $ 0.025 0.004 ?0.64 1.000 — — — —
$ {\theta _{{d5}}} $ 0.026 0.006 ?0.50 ?0.120 1.00 — — —
$ {\theta _{{d6}}} $ ?0.461 0.118 ?0.61 0.200 0.42 1.00 — —
$ {\theta _{{d10}}} $ 0.232 0.065 ?0.32 0.690 ?0.19 0.24 1.000 —
$ {\sigma _{{d}}} $ 0.179 0.012 ?0.03 0.008 0.03 0.01 ?0.007 1.0
表 5  顶层位移概率模型参数的后验分布信息
图 5  所提概率模型所建20层钢框架的4类地震需求概率密度曲线
图 6  不同方法计算的20层钢框架结构易损性曲线对比
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