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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (6): 1080-1089    DOI: 10.3785/j.issn.1008-973X.2023.06.003
    
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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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     
Received: 16 May 2022      Published: 30 June 2023
CLC:  P 315.9  
Fund:  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）
Corresponding Authors: Long-jun XU     E-mail: zgc011@126.com;xulongjun80@163.com
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Guo-chen ZHAO
Long-jun XU
Jia-jun DU
Jing-zhou ZHU
Xing-ji ZHU
Li-li XIE
Cite this article:

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.

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


脉冲型地震动作用下钢框架结构地震需求概率模型

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 
Fig.1 Comparison of maximum bottom shear force obtained by different methods
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
Tab.1 Coefficients of variations and standard deviations of maximum bottom shear force probabilistic model parameters in optimization process
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
Tab.2 Posterior statistics of parameters for maximum bottom shear force probabilistic model
Fig.2 Comparison of maximum bottom moment obtained by different methods
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
Tab.3 Posterior statistics of parameters for maximum bottom moment probabilistic model
Fig.3 Comparison of maximum story drift obtained by different methods
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
Tab.4 Posterior statistics of parameters for maximum story drift probabilistic model
Fig.4 Comparison of top displacement obtained by different methods
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
Tab.5 Posterior statistics of parameters for top displacement probabilistic model
Fig.5 Probability density curves of four types of seismic demand for 20-story steel frame constructed by proposed probability model
Fig.6 Comparison of fragility curves obtained by different methods for 20-story frame structure
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