基于纤维梁柱单元的桥梁墩柱地震反应模拟方法研究
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摘要
为讨论利用纤维梁柱单元进行钢筋混凝土桥墩地震反应分析的建模方法,分别以4个悬臂式单柱墩和1个双柱墩拟静力加载试验,以及1个悬臂式单柱墩的振动台试验结果为依据,基于OpenSees数值分析平台建立了桥墩的地震反应分析模型。通过改变单元数量,分析了基于力的纤维梁柱单元和基于位移的纤维梁柱单元对桥墩地震反应的模拟精度。结果表明:对悬臂式单柱墩的拟静力和振动台试验,可沿墩高仅建立1个基于力的纤维梁柱单元,并在墩底串联1个考虑纵筋塑性渗透和粘结滑移的转动弹簧单元,即可获得很好的模拟结果。当采用基于位移的纤维梁柱单元时,应沿墩高至少建立2个单元,且塑性铰区至少有1个,才能保证获得较高的模拟精度。对双柱墩拟静力试验,采用基于力的纤维梁柱单元建模,沿每个墩高建立2个单元即可;以基于位移的纤维梁柱单元建模,建议沿每个墩高建立3个单元,且其中2个单元布置在塑性铰区。当数值模型可对静力滞回曲线取得很好的模拟结果后,该模型一般可对动力作用下墩顶最大位移和墩底最大剪力进行较为准确的模拟,但对墩顶残余位移的模拟精度无法保证。
To investigate the modeling method for the seismic response analysis of the reinforced concrete bridge piers by using fiber beam-column elements, different models for the piers were built based on OpenSees platform. The effectiveness of the models were verified by comparing the simulation results with the quasi-static test results of four cantilever single column piers and one double-column bridge bent, and the shaking table test results of one cantilever single column pier. By changing the number of the fiber beam-column elements, the simulation accuracy of the models using either force-based or displacement-based beam-column element was discussed. It is shown from the comparison results for both the quasi-static and shaking table tests of the cantilever column pier that only one force-based beam-column element with a rotation spring element to consider the longitudinal bar penetration and bond slip deformation is enough. While at least two displacement-based beam-column elements with one in the plastic hinge zone should be used to ensure the accuracy of the model. For the quasi-static test results of a double-column bent, only one force-based beam-column element along the length of each pier will be enough to model the behavior of the bent, while at least three displacement-based beam-column elements with two in the plastic hinge regions of each pier is required. When the model is able to reasonably simulate the hysteretic curve of the pier under quasi-static test, the model usually gives a good simulation on the maximum displacement and the maximum shear force, but the simulation accuracy for the residual displacement of the pier may not be guaranteed.
To investigate the modeling method for the seismic response analysis of the reinforced concrete bridge piers by using fiber beam-column elements, different models for the piers were built based on OpenSees platform. The effectiveness of the models were verified by comparing the simulation results with the quasi-static test results of four cantilever single column piers and one double-column bridge bent, and the shaking table test results of one cantilever single column pier. By changing the number of the fiber beam-column elements, the simulation accuracy of the models using either force-based or displacement-based beam-column element was discussed. It is shown from the comparison results for both the quasi-static and shaking table tests of the cantilever column pier that only one force-based beam-column element with a rotation spring element to consider the longitudinal bar penetration and bond slip deformation is enough. While at least two displacement-based beam-column elements with one in the plastic hinge zone should be used to ensure the accuracy of the model. For the quasi-static test results of a double-column bent, only one force-based beam-column element along the length of each pier will be enough to model the behavior of the bent, while at least three displacement-based beam-column elements with two in the plastic hinge regions of each pier is required. When the model is able to reasonably simulate the hysteretic curve of the pier under quasi-static test, the model usually gives a good simulation on the maximum displacement and the maximum shear force, but the simulation accuracy for the residual displacement of the pier may not be guaranteed.
引文
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[9] 孙治国,郭迅,王东升,等.钢筋混凝土空心墩延性变形能力分析[J].铁道学报,2012,34(1):91-96.SUN Zhiguo,GUO Xun,WANG Dongsheng,et al.Analysis on ductile deformability of hollow reinforced concrete bridge piers [J].Journal of the China Railway Scoeity,2012,34(1):91-96.(in Chinese)
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[12] LIU KY,WITARTO W,CHANG KC.Composed analytical models for seismic assessment of reinforced concrete bridge columns [J].Earthquake Engineering and Structural Dynamics,2015,44(2):265-281.
[13] 孟春光,吕西林.柔度法纤维模型在方管混凝土柱滞回仿真中的应用[J].地震工程与工程振动,2009,29(4):62-69.MENG Chunguang,LV Xilin.Application of flexibility-based fiber-model beam-column element in simulation analysis of CFRT columns [J].Journal of Earthquake Engineering and Engineering Vibration,2009,29(4):62-69.(in Chinese)
[14] ANDRAWES B,SHIN M,WIERSCHEM N.Active confinement of reinforced concrete bridge columns using shape memory alloys [J].Journal of Bridge Engineering,ASCE,2010,15(1):81-89.
[15] SHIN M,ANDRAWES B.Parametric study of RC bridge columns actively confined with shape memory alloy spirals under lateral cyclic loading [J].Journal of Bridge Engineering,ASCE,2014,19(10):04014040.
[16] YANG Y S,TSAI KC,ELNASHAI AS,et al.An online optimization method for bridge dynamic hybrid simulations [J].Simulation Modelling Practice and Theory,2012,28:42-54.
[17] KO Y F,PHUNG C.Nonlinear static cyclic pushover analysis for flexural failure of reinforced concrete bridge columns with combined damage mechanisms [J].ActaMechanica,2014,225(2):477-492.
[18] 李忠献,李杨,李宁.RC桥墩抗震性能分析模型与验证[J].地震工程与工程振动,2014,34(1):71-80.LI Zhongxian,LI Yang,LI Ning.Seismic analysis model of RC bridge piers:simulation and verification [J].Journal of Earthquake Engineering and Engineering Vibration,2014,34(1):71-80.(in Chinese)
[19] ZHAO J,SRITHARAN S.Modeling of strain penetration effects in fiber-based analysis of reinforced concrete structures [J].ACI Structural Journal,2007,104(2):133-141.
[20] 司炳君,李宏男,王东升,等.基于位移设计的钢筋混凝土桥墩抗震性能试验研究(I):拟静力试验[J].地震工程与工程振动,2008,28(1):123-129.SI Bingjun,LI Hongnan,WANG Dongsheng.et al.Experimental evaluation of the seismic performance of reinforced concrete bridge piers designed on the base of displacement (I):Quasi-static test [J].Journal of Earthquake Engineering and Engineering Vibration,2008,28(1):123-129.(in Chinese)
[21] 李贵乾.钢筋混凝土桥墩抗震性能试验研究及数值分析[D].重庆:重庆交通大学,2010.LI Guiqian.Experimental study and numerical analysis on seismic performance of reinforced concrete bridge columns [D].Chongqing:Chongqing Jiaotong University,2010.(in Chinese)
[22] ELGAWADY M,SHALAN A.Seismic behavior of self-centering precast segmental bridge Bents [J].Journal of Bridge Engineering,ASCE,2011,16(3):328-339.
[23] 赵泰儀,孙治国,王东升,等.RC桥墩残余位移模拟的参数敏感性分析[J].振动与冲击,2018,37(15):251-260.ZHAO Taiyi,SUN Zhiguo,WANG Dongsheng,et al.Parameter sensitivity analysis in simulation of residual displacement of RC bridge piers [J].Journal of Vibration and Shock,2018,37(15):251-260.(in Chinese)
[2] 黄宗明,陈滔.基于有限单元柔度法和刚度法的非线性梁柱单元比较研究[J].工程力学,2003,20(5):24-31.HUANG Zongming,CHEN Tao.Comparison between flexibility-based and stiffness-based nonlinear beam-column elements [J].Engineering Mechanics,2003,20(5):24-31.(in Chinese)
[3] TAUCER FF,SPACONE E,FILIPPOU FC.A fiber beam-column element for seismic response analysis of reinforced concrete structures [R].Report No.UCB/EERC-91/17,University of California,Berkeley,1991.
[4] COLEMAN J,SPACONE E.Localization issues in force-based frame elements [J].Journal of Structural Engineering,ASCE,2001,127(11):1257-1267.
[5] 赫中营,叶爱君.力法非线性梁柱单元的合理单元长度划分[J].工程力学,2014,31(7):178-184,198.HE Zhongying,YE Aijun.Reasonable discrete element length of force-based nonlinear beam-column elements [J].Engineering Mechanics,2014,31(7):178-184,198.(in Chinese)
[6] 聂利英,李建中,范立础.弹塑性纤维梁柱单元及其单元参数分析[J].工程力学,2004,21(3):15-20.NIE Liying,LI Jianzhong,FAN Lichu.Elastic-plastic fiber beam-column element and its parametric analysis [J].Engineering Mechanics,2004,21(3):15-20.(in Chinese)
[7] BERRY MP,EBERHARD MO.Performance modeling strategies for modern reinforced concrete bridge columns [R].PEER Report 2007/07,Pacific Earthquake Engineering Research Center,University of California,Berkeley,2008.
[8] 艾庆华,王东升,向敏.基于纤维单元的钢筋混凝土桥墩地震损伤评价[J].计算力学学报,2011,28(5):737-742.AI Qinghua,WANG Dongsheng,XIANG Min.Seismic damage evaluation of RC bridge columns based on fiber elements [J].Chinese Journal of Computational Mechanics,2011,28(5):737-742.(in Chinese)
[9] 孙治国,郭迅,王东升,等.钢筋混凝土空心墩延性变形能力分析[J].铁道学报,2012,34(1):91-96.SUN Zhiguo,GUO Xun,WANG Dongsheng,et al.Analysis on ductile deformability of hollow reinforced concrete bridge piers [J].Journal of the China Railway Scoeity,2012,34(1):91-96.(in Chinese)
[10] ELGAMAL A,YAN L,YANG Z,et al.Three-dimensional seismic response of humboldt bay bridge-foundation-ground system [J].Journal of Structural Engineering,ASCE,2008,134(7):1165-1176.
[11] TERZIC V,STOJADINOVIC B.Calibration and validation of analytical models for predicting the seismic and axial-load response of circular bridge columns [J].Journal of Bridge Engineering,ASCE,2015,20(9):04014098.
[12] LIU KY,WITARTO W,CHANG KC.Composed analytical models for seismic assessment of reinforced concrete bridge columns [J].Earthquake Engineering and Structural Dynamics,2015,44(2):265-281.
[13] 孟春光,吕西林.柔度法纤维模型在方管混凝土柱滞回仿真中的应用[J].地震工程与工程振动,2009,29(4):62-69.MENG Chunguang,LV Xilin.Application of flexibility-based fiber-model beam-column element in simulation analysis of CFRT columns [J].Journal of Earthquake Engineering and Engineering Vibration,2009,29(4):62-69.(in Chinese)
[14] ANDRAWES B,SHIN M,WIERSCHEM N.Active confinement of reinforced concrete bridge columns using shape memory alloys [J].Journal of Bridge Engineering,ASCE,2010,15(1):81-89.
[15] SHIN M,ANDRAWES B.Parametric study of RC bridge columns actively confined with shape memory alloy spirals under lateral cyclic loading [J].Journal of Bridge Engineering,ASCE,2014,19(10):04014040.
[16] YANG Y S,TSAI KC,ELNASHAI AS,et al.An online optimization method for bridge dynamic hybrid simulations [J].Simulation Modelling Practice and Theory,2012,28:42-54.
[17] KO Y F,PHUNG C.Nonlinear static cyclic pushover analysis for flexural failure of reinforced concrete bridge columns with combined damage mechanisms [J].ActaMechanica,2014,225(2):477-492.
[18] 李忠献,李杨,李宁.RC桥墩抗震性能分析模型与验证[J].地震工程与工程振动,2014,34(1):71-80.LI Zhongxian,LI Yang,LI Ning.Seismic analysis model of RC bridge piers:simulation and verification [J].Journal of Earthquake Engineering and Engineering Vibration,2014,34(1):71-80.(in Chinese)
[19] ZHAO J,SRITHARAN S.Modeling of strain penetration effects in fiber-based analysis of reinforced concrete structures [J].ACI Structural Journal,2007,104(2):133-141.
[20] 司炳君,李宏男,王东升,等.基于位移设计的钢筋混凝土桥墩抗震性能试验研究(I):拟静力试验[J].地震工程与工程振动,2008,28(1):123-129.SI Bingjun,LI Hongnan,WANG Dongsheng.et al.Experimental evaluation of the seismic performance of reinforced concrete bridge piers designed on the base of displacement (I):Quasi-static test [J].Journal of Earthquake Engineering and Engineering Vibration,2008,28(1):123-129.(in Chinese)
[21] 李贵乾.钢筋混凝土桥墩抗震性能试验研究及数值分析[D].重庆:重庆交通大学,2010.LI Guiqian.Experimental study and numerical analysis on seismic performance of reinforced concrete bridge columns [D].Chongqing:Chongqing Jiaotong University,2010.(in Chinese)
[22] ELGAWADY M,SHALAN A.Seismic behavior of self-centering precast segmental bridge Bents [J].Journal of Bridge Engineering,ASCE,2011,16(3):328-339.
[23] 赵泰儀,孙治国,王东升,等.RC桥墩残余位移模拟的参数敏感性分析[J].振动与冲击,2018,37(15):251-260.ZHAO Taiyi,SUN Zhiguo,WANG Dongsheng,et al.Parameter sensitivity analysis in simulation of residual displacement of RC bridge piers [J].Journal of Vibration and Shock,2018,37(15):251-260.(in Chinese)