基于Bayesian理论的弯剪破坏钢筋混凝土柱变形能力概率模型
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摘要
为了准确预测地震作用下弯剪破坏钢筋混凝土(RC)柱的变形能力,基于Bayesian理论提出了一种建立柱类构件变形能力概率模型的方法。首先对已有RC柱变形能力公式进行评价并选作先验模型,再借助美国PEER柱抗震性能试验数据库中发生弯剪破坏的20根矩形截面RC墩柱的拟静力试验数据作为客观认识,应用Bayesian参数估计方法综合这两类信息进行推断,修正先验模型的偏差从而建立反复荷载作用下弯剪破坏RC柱变形能力的概率模型;采用Bayesian方法剔除影响修正效果不显著的因素以获得模型简化,达到对先验模型的动态更新。最后,讨论了不同形式修正项对修正效果的影响。结果表明,Bayesian方法既继承了先验信息的完备性,又利用了试验数据的准确性,建议的概率模型较已有公式能够更准确地预测弯剪破坏RC柱的变形能力,从而为RC柱抗震设计或评估中考虑能力不确定性提供了便利。
In order to predict the deformation capacity of reinforced concrete columns(RC) failed in flexural-shear under seismic loading, a methodology to construct probabilistic deformation capacity models of columns is developed based on Bayesian theory. The prior models are proposed based on evaluating the biases of base deterministic models. And, the quasi-static test data of 20 rectangular RC columns failed in flexural-shear were collected from PEER-Structural Performance Database and used as objective knowledge. Two types of information, epistemic information and experimental information, are synthesized by Bayesian estimation method and inferred to update prior models. The probabilistic models for the deformation capacity of RC columns failed in flexural-shear under cyclic loading are constructed. Subsequently, the probabilistic models are simplified by using the stepwise procedure to delete unimportant terms and the dynamic updating of prior models is achieved.Then, the effect of different correction items is discussed. The results show that the approach inherits the completeness of prior models and the accuracy of experimental data information. Therefore, it could more accurately predict the deformation capacity of RC columns failed in flexural-shear, which is convenient to consider the capacity uncertainty in the aseismic design or in the evaluation of RC column.
In order to predict the deformation capacity of reinforced concrete columns(RC) failed in flexural-shear under seismic loading, a methodology to construct probabilistic deformation capacity models of columns is developed based on Bayesian theory. The prior models are proposed based on evaluating the biases of base deterministic models. And, the quasi-static test data of 20 rectangular RC columns failed in flexural-shear were collected from PEER-Structural Performance Database and used as objective knowledge. Two types of information, epistemic information and experimental information, are synthesized by Bayesian estimation method and inferred to update prior models. The probabilistic models for the deformation capacity of RC columns failed in flexural-shear under cyclic loading are constructed. Subsequently, the probabilistic models are simplified by using the stepwise procedure to delete unimportant terms and the dynamic updating of prior models is achieved.Then, the effect of different correction items is discussed. The results show that the approach inherits the completeness of prior models and the accuracy of experimental data information. Therefore, it could more accurately predict the deformation capacity of RC columns failed in flexural-shear, which is convenient to consider the capacity uncertainty in the aseismic design or in the evaluation of RC column.
引文
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[11]马颖,孙治国,王东升,等.基于变形能力的钢筋混凝土桥墩约束箍筋用量评价[J].桥梁建设,2014,44(6):57―62.Ma Ying,Sun Zhiguo,Wang Dongsheng,et al.Evaluation of amounts of confining stirrups used for RCbridge columns based on deformation capacity[J].Bridge Construction,2014,44(6):57―62.(in Chinese)
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[14]余波,陈冰,吴然立.剪切型钢筋混凝土柱抗剪承载力计算的概率模型[J].工程力学,2017,34(7):136―145.Yu Bo,Chen Bing,Wu Ranli.Probabilistic model for shear strength of shear-critical reinforced concrete columns[J].Engineering Mechanics,2017,34(7):136―145.(in Chinese)
[15]张家瑞,魏凯,秦顺全.基于贝叶斯更新的深水桥墩波浪动力响应概率模型[J].工程力学,2018,35(8):138―143,171.Zhang Jiarui,Wei Kai,Qin Shunquan.A Bayesian updating based probabilistic model for the dynamic response of deepwater bridge piers under wave loading[J].Engineering Mechanics,2018,35(8):138―143,171.(in Chinese)
[16]Gardoni P,Kiureghian A D,Mosalam K M.Probabilistic capacity models and fragility estimates for reinforced concrete columns based on experimental observations[J].Journal of Engineering Mechanics,ASCE,2002,128(10):1024―1038.
[17]Sasani M.Life-safety and near-collapse capacity models for seismic shear behavior of reinforced concrete columns[J].ACI Structural Journal,2007,104(1):30―38.
[18]Zhu L.Probabilistic drift capacity models for reinforced concrete columns[D].Vancouver:University of British Columbia,2005.
[19]Zhu L,Elwood K J,Haukaas T.Classification and seismic safety evaluation of existing reinforced concrete columns[J].Journal of Structural Engineering,ASCE,2007,133(9):1316―1330.
[20]卓卫东,曾武华.矩形RC桥墩变形能力概率模型[J].工程力学,2015,32(1):57―63.Zhuo Weidong,Zeng Wuhua.Probabilistic deformation capacity for rectangular bridge columns[J].Engineering Mechanics,2015,32(1):57―63.(in Chinese)
[21]John A Rice,田金方.数理统计与数据分析[M].北京:机械工业出版社,2016:97―206.John A Rice,Tian Jinfang.Mathematical statistics and data analysis[M].Beijing:China Machine Press,2016:97―206.(in Chinese)
[22]Rao C R,Toutenburg H.Linear models:least squares and alternatives[M].New York:Springer,1997.
[23]Box G E P,Tiao G C.Bayesian inference in statistical analysis[M].London:Addison-Wesley,1992.
[24]王东升,司炳君,孙治国,等.地震作用下钢筋混凝土桥墩塑性铰区抗剪强度试验[J].中国公路学报,2011,24(2):34―41.Wang Dongsheng,Si Bingjun,Sun Zhiguo,et al.Experiment on shear strength of reinforced concrete bridge column in plastic hinge zone under seismic effect[J].China Journal of Highway and Transport,2011,24(2):34―41.(in Chinese)
[25]孙治国,王东升,杜修力,等.钢筋混凝土桥墩塑性铰区约束箍筋用量研究[J].中国公路学报,2010,23(3):48―57.Sun Zhiguo,Wang Dongsheng,Du Xiuli,et al.Research on amount of confining reinforcement in potential plastic hinge regions of RC bridge columns[J].China Journal of Highway and Transport,2010,23(3):48―57.(in Chinese)
[26]贡金鑫,魏巍巍,胡家顺.中美欧混凝土结构设计[M].北京:中国建筑工业出版社,2007:74―77.Gong Jinxin,Wei Weiwei,Hu Jiashun.Concrete structure design in China USA and Europe[M].Bei Jing:China Architecture&Building Press,2007:74―77.(in Chinese)
[27]Zhang Q,Gong J X,Ma Y.Seismic shear strength and deformation of RC columns failed in flexural shear[J].Magazine of Concrete Research,2014,66(5):234―248.
[2]王东升,郭迅,孙治国,等.汶川大地震公路桥梁震害初步调查[J].地震工程与工程振动,2009,29(3):84―94.Wang Dongsheng,Guo Xun,Sun Zhiguo,et al.Damage to highway bridges during Wenchuan Earthquake[J].Earthquake Engineering and Engineering Vibration,2009,29(3):84―94.(in Chinese)
[3]ASCE/SEI 41-06.Seismic rehabilitation of existing buildings[S].American Society of Civil Engineers,Reston,Virginia,2007.
[4]European Standard EN 1998-3,Eurocode 8:design of structures for earthquake resistance-part 3:assessment and retrofitting of buildings[S].Comite Europeen de Normalisation,Brussels,2005.
[5]Paultre P,Legeron F.Confinement reinforcement design for reinforced concrete columns[J].Journal of Structural Engineering,ASCE,2008,134(5):738―749.
[6]禚一,李忠献.钢筋混凝土纤维梁柱单元实用模拟平台[J].工程力学,2011,28(1):102―108,127.Zhuo Yi,Li Zhongxian.A practical simulation platfoem of reinforced concrete fiber beam-column element[J].Engineering Mechanics,2011,28(1):102―108,127.(in Chinese)
[7]孙治国,陈灿,司炳君,等.考虑非线性剪切效应的RC桥墩抗震分析模型[J].工程力学,2015,32(5):28―36,50.Sun Zhiguo,Chen Can,Si Bingjun,et al.Seismic analysis model considering nonlinear shear effect for RCbridge piers[J].Engineering Mechanics,2015,32(5):28―36,50.(in Chinese)
[8]Ma Y,Gong J X.Seismic failure modes and deformation capacity of reinforced concrete columns under cyclic loads[J].Periodica Polytechnica-Civil Engineering,2018,62(1):80―91.
[9]Elwood K J,Moehle J P.Drift capacity of reinforced concrete columns with light transverse reinforcement[J].Earthquake Spectra,2005,21(1):71―89.
[10]熊朝晖,潘德恩.钢筋混凝土框架柱侧向变形能力的研究[J].地震工程与工程振动,2001,21(2):103―108.Xiong Zhaohui,Pan Deen.Study on lateral deformability of reinforced concrete frame columns[J].Earthquake Engineering and Engineering Vibration,2001,21(2):103―108.(in Chinese)
[11]马颖,孙治国,王东升,等.基于变形能力的钢筋混凝土桥墩约束箍筋用量评价[J].桥梁建设,2014,44(6):57―62.Ma Ying,Sun Zhiguo,Wang Dongsheng,et al.Evaluation of amounts of confining stirrups used for RCbridge columns based on deformation capacity[J].Bridge Construction,2014,44(6):57―62.(in Chinese)
[12]Choe D E,Gardoni P,Rosowsky D.Closed-form fragility estimates,parameter sensitivity,and Bayesian updating for RC columns[J].Journal of Engineering Mechanics,ASCE,2007,133(7):833―843.
[13]Tabandeh A,Gardoni P.Probabilistic capacity models and fragility estimates for RC columns retrofitted with FRP composites[J].Engineering Structures,2014,74(1):13―22.
[14]余波,陈冰,吴然立.剪切型钢筋混凝土柱抗剪承载力计算的概率模型[J].工程力学,2017,34(7):136―145.Yu Bo,Chen Bing,Wu Ranli.Probabilistic model for shear strength of shear-critical reinforced concrete columns[J].Engineering Mechanics,2017,34(7):136―145.(in Chinese)
[15]张家瑞,魏凯,秦顺全.基于贝叶斯更新的深水桥墩波浪动力响应概率模型[J].工程力学,2018,35(8):138―143,171.Zhang Jiarui,Wei Kai,Qin Shunquan.A Bayesian updating based probabilistic model for the dynamic response of deepwater bridge piers under wave loading[J].Engineering Mechanics,2018,35(8):138―143,171.(in Chinese)
[16]Gardoni P,Kiureghian A D,Mosalam K M.Probabilistic capacity models and fragility estimates for reinforced concrete columns based on experimental observations[J].Journal of Engineering Mechanics,ASCE,2002,128(10):1024―1038.
[17]Sasani M.Life-safety and near-collapse capacity models for seismic shear behavior of reinforced concrete columns[J].ACI Structural Journal,2007,104(1):30―38.
[18]Zhu L.Probabilistic drift capacity models for reinforced concrete columns[D].Vancouver:University of British Columbia,2005.
[19]Zhu L,Elwood K J,Haukaas T.Classification and seismic safety evaluation of existing reinforced concrete columns[J].Journal of Structural Engineering,ASCE,2007,133(9):1316―1330.
[20]卓卫东,曾武华.矩形RC桥墩变形能力概率模型[J].工程力学,2015,32(1):57―63.Zhuo Weidong,Zeng Wuhua.Probabilistic deformation capacity for rectangular bridge columns[J].Engineering Mechanics,2015,32(1):57―63.(in Chinese)
[21]John A Rice,田金方.数理统计与数据分析[M].北京:机械工业出版社,2016:97―206.John A Rice,Tian Jinfang.Mathematical statistics and data analysis[M].Beijing:China Machine Press,2016:97―206.(in Chinese)
[22]Rao C R,Toutenburg H.Linear models:least squares and alternatives[M].New York:Springer,1997.
[23]Box G E P,Tiao G C.Bayesian inference in statistical analysis[M].London:Addison-Wesley,1992.
[24]王东升,司炳君,孙治国,等.地震作用下钢筋混凝土桥墩塑性铰区抗剪强度试验[J].中国公路学报,2011,24(2):34―41.Wang Dongsheng,Si Bingjun,Sun Zhiguo,et al.Experiment on shear strength of reinforced concrete bridge column in plastic hinge zone under seismic effect[J].China Journal of Highway and Transport,2011,24(2):34―41.(in Chinese)
[25]孙治国,王东升,杜修力,等.钢筋混凝土桥墩塑性铰区约束箍筋用量研究[J].中国公路学报,2010,23(3):48―57.Sun Zhiguo,Wang Dongsheng,Du Xiuli,et al.Research on amount of confining reinforcement in potential plastic hinge regions of RC bridge columns[J].China Journal of Highway and Transport,2010,23(3):48―57.(in Chinese)
[26]贡金鑫,魏巍巍,胡家顺.中美欧混凝土结构设计[M].北京:中国建筑工业出版社,2007:74―77.Gong Jinxin,Wei Weiwei,Hu Jiashun.Concrete structure design in China USA and Europe[M].Bei Jing:China Architecture&Building Press,2007:74―77.(in Chinese)
[27]Zhang Q,Gong J X,Ma Y.Seismic shear strength and deformation of RC columns failed in flexural shear[J].Magazine of Concrete Research,2014,66(5):234―248.