矩形RC桥墩变形能力概率模型
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摘要
桥墩是桥梁抗侧力体系中的关键构件。为实现基于概率和性能的桥梁抗震设计的多级性能目标,有必要给出桥墩在不同性能极限状态下的概率能力。基于已有研究工作,将RC桥墩的抗震性能水平划分为五个等级,并定义了相应的性能极限状态。采用等效集中塑性铰理论,推导并建立了各性能极限状态下RC墩柱变形能力的确定性计算公式;基于183个矩形RC墩柱试件的拟静力试验结果,通过多元回归分析,确定了各计算公式中与轴压比、长细比和配箍特征值等设计参数相关的待定系数。基于确定性计算模型和拟静力试验结果,考虑认知不确定性,建立了矩形RC墩柱变形能力的概率模型。通过实例分析,表明该模型可用于基于概率和性能的桥梁抗震设计和抗震评估。
Piers are key components in a lateral force resisting system of bridge structures. To implement the multiple performance objectives of probability-based and performance-based seismic design for bridge structures, the probabilistic capacity of piers need to be calculated at various performance limit states. Based on previous research works, 5 seismic performance levels and 4 corresponding performance limit states are defined for RC bridge columns. The deterministic formula for deformation capacities of RC bridge columns at each performance limit state is derived from equivalent plastic hinge theory. On the basis of quasi-static test results of 183 rectangular flexure dominant RC bridge columns, the coefficients associated with the axial-load ratio, aspect ratio and stirrup characteristic value in the formula are determined by a multiple regression analysis. Considering the epistemic uncertainty of the deterministic formula, a probabilistic deformation capacity model for rectangular RC bridge columns is developed based on both the deterministic formula and the quasi-static test results. A case study for a typical RC bridge column shows that the probabilistic model can be applied to the probability-based and performance-based seismic design and the evaluation of bridge structures.
Piers are key components in a lateral force resisting system of bridge structures. To implement the multiple performance objectives of probability-based and performance-based seismic design for bridge structures, the probabilistic capacity of piers need to be calculated at various performance limit states. Based on previous research works, 5 seismic performance levels and 4 corresponding performance limit states are defined for RC bridge columns. The deterministic formula for deformation capacities of RC bridge columns at each performance limit state is derived from equivalent plastic hinge theory. On the basis of quasi-static test results of 183 rectangular flexure dominant RC bridge columns, the coefficients associated with the axial-load ratio, aspect ratio and stirrup characteristic value in the formula are determined by a multiple regression analysis. Considering the epistemic uncertainty of the deterministic formula, a probabilistic deformation capacity model for rectangular RC bridge columns is developed based on both the deterministic formula and the quasi-static test results. A case study for a typical RC bridge column shows that the probabilistic model can be applied to the probability-based and performance-based seismic design and the evaluation of bridge structures.
引文
[1]Deierlein G G,Krawinkler H,Cornell C A.A framework for performance-based earthquake engineering[C].Proceedings of 2003 Pacific Conference on Earthquake Engineering.Christchurch,New Zealand,CD-ROOM,Elsevier,2003:1―8.
[2]Porter K A.An overview of PEER’s performance-based earthquake engineering methodology[C].Proceedings of Ninth International Conference on Applications of Statistics and Probability in Civil Engineering,San Francisco,2003:1―8.
[3]Moehle J,Deierlein G G.A framework methodology for performance-based engineering[C].Proceedings of 13th World Conference on Earthquake Engineering.Vancouver B C Canada,CD-ROOM,Elsevier,2004:1―6.
[4]刘洪兵,王君杰,孙利民,范立础.钢筋混凝土桥墩截面能力的概率分析[J].工程力学,2005,22(6):104―111.Liu Hongbing,Wang Junjie,Sun Limin,Fan Lichu.Probability characteristics of cross-section capacity of RC piers[J].Engineering Mechanics,2005,22(6):104―111.(in Chinese)
[5]Lu Y,Gu X,Guan J.Probabilistic drift limits and performance evaluation of reinforced concrete columns[J].Journal of Structural Engineering,2005,131(6):966―978.
[6]王建民,朱晞.圆截面RC桥墩曲率极限状态和延性的概率分析[J].土木工程学报,2006,39(12):88―94.Wang Jianmin,Zhu Xi.Probability analysis of the curvature limit state and ductility of circular RC bridge piers[J].China Civil Engineering Journal,2006,39(12):88―94.(in Chinese)
[7]冯清海,袁万城.基于ANN-MC的钢筋混凝土桥墩截面能力概率特征统计方法[J].武汉理工大学学报,2008,32(6):990―993.Fen Qinghai,Yuan Wancheng.Study of probability characteristics of cross-section capability of RC pier based on ANN-MC[J].Journal of Wuhan University of Technology,2008,32(6):990―993.(in Chinese)
[8]孙颖,卓卫东,房贞政.规则桥梁抗震性能水准的定义及其量化描述[J].地震工程与工程振动,2011,31(5):104―112.Sun Ying,Zhuo Weidong,Fang Zhenzheng.Definition and quantified description of seismic performance levels for regular bridges[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(5):104―112.(in Chinese)
[9]陆本燕,刘伯权,邢国华,吴涛.桥梁结构基于性能的抗震设防目标与性能指标研究[J].工程力学,2011,28(11):96―103.Lu Benyan,Liu Boquan,Xing Guohua,Wu Tao.Study on fortification criterion and quantified performance index for reinforced concrete bridge structures in performance-based seismic design[J].Engineering Mechanics,2011,28(11):96―103.(in Chinese)
[10]Hose Y D,Seible F.Performance evaluation database for concrete bridge components and systems under simulated seismic loads[R].Berkeley:Report No.PEER-1999/11,PEER&University of California,Berkeley,1999.
[11]Smith K G.Innovation in earthquake ressistant concrete strutcture design philosophies:a century of progress since Hennebiques patent[J].Engineering Structure,2001,23(1):72―81.
[12]王东升,李宏男,赵颖华,等.钢筋混凝土桥墩基于位移的抗震设计方法[J].土木工程学报,2006,39(10):80―86.Wang Dongsheng,Li Hongnan,Zhao Yinghua,et al.Displacement-based seismic design of RC bridge[J].China Civil Engineering Journal,2006,39(10):80―86.(in Chinese)
[13]邹中权.桥梁结构抗震性能概率性分析方法研究[D].长沙:中南大学,2010.Zou Zhongquan.On probabilistic method for performance-based seismic analysis of bridge structures[D].Changsha:Central South University,2010.(in Chinese)
[14]Park R,Paulay T.Reinforced concrete structuresn[M].New York:John Wiley&Sons Inc,1975:236―264.
[15]Paulay T,Priestley M J N.Seismic design of reinforced concrete and masonry buildings[M].New York:John Wiley and Sons Inc,1992:135―145.
[16]孙治国,王东升,郭迅,李晓莉.钢筋混凝土墩柱等效塑性铰长度研究[J].中国公路学报,2011,24(5):56―64.Sun Zhiguo,Wang Dongsheng,Guo Xun,Li Xiaoli.Research on equivalent plastic hinge length of reinforced concrete bridge column[J].China Journal of Highway and Transport,2011,24(5):56―64.(in Chinese)
[17]Berry M P,Eberhard M O.Performance models for flexural damage in reinforce concrete columns[R].Berkeley:Pacific Earthquake Engineering Research Center Report,2003.
[18]CALTRANS SDC 1.6.Caltrans Seismic Design Criteria[S].2010.
[19]Tassios T P.Response of RC critical regions under large amplitude reversed actions[R].Paris,CEB,1983.
[20]Eberhard M.The structural performance database[DB].http://nisee.berkeley.edu/spd/index.html,2003.
[21]Kawashima K.Cyclic loading test data of reinforced concrete bridge piers[DB].http://seismic.cv.titech.ac.jp/en/titdata/titdata.html,2006.
[22]卓卫东.桥梁延性抗震设计[D].上海:同济大学,2000.Zhuo Weidong.Study on seismic design for ductility of bridges[D].Shanghai:Tong Ji University,2000.(in Chinese)
[23]Syntzirma D V,Pantazopoulou S J,Aschheim M.Load-history effects on deformation capacity of flexural members limited by bar buckling[J].Journal of Structural Engineering,2010,136(1):1―11.
[24]Goodnight J C,Kowalsky M J,Nau J M.Experimental observations on the effect of load history on performance limit states of circular bridge columns[C].Proceedings of 15th World Conference on Earthquake Engineering.Lisbon Portugal,CD-ROOM,Elsecier,2012:1―10.
[25]Ang A H S,Tang W H.Probability concepts in engineering:emphasis on applications in civil and environmental engineering[M].New York:John Wiley and Sons Inc,2007:293―296.
[2]Porter K A.An overview of PEER’s performance-based earthquake engineering methodology[C].Proceedings of Ninth International Conference on Applications of Statistics and Probability in Civil Engineering,San Francisco,2003:1―8.
[3]Moehle J,Deierlein G G.A framework methodology for performance-based engineering[C].Proceedings of 13th World Conference on Earthquake Engineering.Vancouver B C Canada,CD-ROOM,Elsevier,2004:1―6.
[4]刘洪兵,王君杰,孙利民,范立础.钢筋混凝土桥墩截面能力的概率分析[J].工程力学,2005,22(6):104―111.Liu Hongbing,Wang Junjie,Sun Limin,Fan Lichu.Probability characteristics of cross-section capacity of RC piers[J].Engineering Mechanics,2005,22(6):104―111.(in Chinese)
[5]Lu Y,Gu X,Guan J.Probabilistic drift limits and performance evaluation of reinforced concrete columns[J].Journal of Structural Engineering,2005,131(6):966―978.
[6]王建民,朱晞.圆截面RC桥墩曲率极限状态和延性的概率分析[J].土木工程学报,2006,39(12):88―94.Wang Jianmin,Zhu Xi.Probability analysis of the curvature limit state and ductility of circular RC bridge piers[J].China Civil Engineering Journal,2006,39(12):88―94.(in Chinese)
[7]冯清海,袁万城.基于ANN-MC的钢筋混凝土桥墩截面能力概率特征统计方法[J].武汉理工大学学报,2008,32(6):990―993.Fen Qinghai,Yuan Wancheng.Study of probability characteristics of cross-section capability of RC pier based on ANN-MC[J].Journal of Wuhan University of Technology,2008,32(6):990―993.(in Chinese)
[8]孙颖,卓卫东,房贞政.规则桥梁抗震性能水准的定义及其量化描述[J].地震工程与工程振动,2011,31(5):104―112.Sun Ying,Zhuo Weidong,Fang Zhenzheng.Definition and quantified description of seismic performance levels for regular bridges[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(5):104―112.(in Chinese)
[9]陆本燕,刘伯权,邢国华,吴涛.桥梁结构基于性能的抗震设防目标与性能指标研究[J].工程力学,2011,28(11):96―103.Lu Benyan,Liu Boquan,Xing Guohua,Wu Tao.Study on fortification criterion and quantified performance index for reinforced concrete bridge structures in performance-based seismic design[J].Engineering Mechanics,2011,28(11):96―103.(in Chinese)
[10]Hose Y D,Seible F.Performance evaluation database for concrete bridge components and systems under simulated seismic loads[R].Berkeley:Report No.PEER-1999/11,PEER&University of California,Berkeley,1999.
[11]Smith K G.Innovation in earthquake ressistant concrete strutcture design philosophies:a century of progress since Hennebiques patent[J].Engineering Structure,2001,23(1):72―81.
[12]王东升,李宏男,赵颖华,等.钢筋混凝土桥墩基于位移的抗震设计方法[J].土木工程学报,2006,39(10):80―86.Wang Dongsheng,Li Hongnan,Zhao Yinghua,et al.Displacement-based seismic design of RC bridge[J].China Civil Engineering Journal,2006,39(10):80―86.(in Chinese)
[13]邹中权.桥梁结构抗震性能概率性分析方法研究[D].长沙:中南大学,2010.Zou Zhongquan.On probabilistic method for performance-based seismic analysis of bridge structures[D].Changsha:Central South University,2010.(in Chinese)
[14]Park R,Paulay T.Reinforced concrete structuresn[M].New York:John Wiley&Sons Inc,1975:236―264.
[15]Paulay T,Priestley M J N.Seismic design of reinforced concrete and masonry buildings[M].New York:John Wiley and Sons Inc,1992:135―145.
[16]孙治国,王东升,郭迅,李晓莉.钢筋混凝土墩柱等效塑性铰长度研究[J].中国公路学报,2011,24(5):56―64.Sun Zhiguo,Wang Dongsheng,Guo Xun,Li Xiaoli.Research on equivalent plastic hinge length of reinforced concrete bridge column[J].China Journal of Highway and Transport,2011,24(5):56―64.(in Chinese)
[17]Berry M P,Eberhard M O.Performance models for flexural damage in reinforce concrete columns[R].Berkeley:Pacific Earthquake Engineering Research Center Report,2003.
[18]CALTRANS SDC 1.6.Caltrans Seismic Design Criteria[S].2010.
[19]Tassios T P.Response of RC critical regions under large amplitude reversed actions[R].Paris,CEB,1983.
[20]Eberhard M.The structural performance database[DB].http://nisee.berkeley.edu/spd/index.html,2003.
[21]Kawashima K.Cyclic loading test data of reinforced concrete bridge piers[DB].http://seismic.cv.titech.ac.jp/en/titdata/titdata.html,2006.
[22]卓卫东.桥梁延性抗震设计[D].上海:同济大学,2000.Zhuo Weidong.Study on seismic design for ductility of bridges[D].Shanghai:Tong Ji University,2000.(in Chinese)
[23]Syntzirma D V,Pantazopoulou S J,Aschheim M.Load-history effects on deformation capacity of flexural members limited by bar buckling[J].Journal of Structural Engineering,2010,136(1):1―11.
[24]Goodnight J C,Kowalsky M J,Nau J M.Experimental observations on the effect of load history on performance limit states of circular bridge columns[C].Proceedings of 15th World Conference on Earthquake Engineering.Lisbon Portugal,CD-ROOM,Elsecier,2012:1―10.
[25]Ang A H S,Tang W H.Probability concepts in engineering:emphasis on applications in civil and environmental engineering[M].New York:John Wiley and Sons Inc,2007:293―296.
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