钢筋混凝土桥墩抗震变形能力研究
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摘要
国内外近期发生的破坏性地震如1989年美国Loma Prieta地震、1994年美国Northridge地震、1995年日本Kobe地震、1999年我国台湾Chi-Chi地震和2008年我国汶川大地震,均对桥墩造成了严重震害。开展钢筋混凝土桥墩抗震问题的研究,对保证桥梁结构抗震安全和交通生命线畅通,具有十分重要的意义。确保桥墩在大震下具有良好的延性和耗能能力,是实现桥梁结构基于位移/性能抗震设计的重要前提。
     本文基于大量试验结果的分析,结合拟静力试验和数值模拟手段,对采用普通和高强钢筋混凝土材料的实心和空心钢筋混凝土桥墩抗震变形能力进行了若干研究,具体包括桥墩延性变形能力及位移相关塑性铰区约束箍筋用量、普通及高强钢筋混凝土墩柱等效塑性铰长度、薄壁空心墩抗震拟静力试验、空心墩变形能力和桥墩弯剪数值分析模型等,主要工作和认识如下:
     1.为研究钢筋混凝土桥墩的延性变形能力和配箍要求,收集整理了国内外进行的234根实心桥墩的抗震拟静力试验数据,基于试验结果对现有桥梁抗震规范保证桥墩延性变形能力的可靠性进行了评价,通过回归分析建立了弯曲破坏桥墩变形能力的表达式;分别以2%和3%极限位移角为设计目标,提出了适用于普通及高强钢筋混凝土桥墩的位移相关塑性铰区约束箍筋用量计算公式并进行了验证。
     2.为评价高强钢筋和混凝土材料的应用对桥墩等效塑性铰长度的影响,收集整理了国内外进行的108根普通及高强钢筋混凝土墩柱等效塑性铰长度试验结果,评价了国内外主要桥梁抗震规范中等效塑性铰长度计算公式的可靠性。通过回归分析讨论了影响墩柱等效塑性铰长度的主要因素并提出了新的表达公式。认为钢筋混凝土墩柱等效塑性铰长度主要与试件高度、加载方向截面宽度和纵筋直径有关。
     3.总结了我国大型桥梁工程中空心桥墩的应用情况,设计了2个矩形薄壁空心墩试件并分别进行了定轴力和变轴力下的抗震拟静力试验。对比分析了试件的破坏过程和最终破坏形态,裂缝宽度,残余位移和抗剪强度等。发现试件倒塌前表现出明显的弯―剪破坏特征,包括弯曲与剪切开裂、混凝土压碎破坏、纵筋屈曲等。由于损伤的逐步累积,试件变形超过2%位移角后,由于薄壁的失稳而引起了突然的倒塌,且变轴力下试件的倒塌破坏更为剧烈。
     4.在总结国内外进行的空心墩抗震试验结果的基础上,分析了弯曲、弯剪和剪切破坏形态下空心墩的变形能力和主要影响因素,认为矩形空心墩变形能力主要与塑性铰区配箍、纵筋配筋、壁厚和轴压比等因素有关,随箍筋、纵筋配筋和壁厚增加而增加,随轴压比增加而减少。讨论了现有规范对保证空心墩变形能力的可靠性,最后基于Caltrans规范给出了不同极限位移角下空心墩塑性铰区约束箍筋用量设计公式。
     5.基于纤维单元模型和修正的压力场理论(The Modified CompressionField Theory, MCFT)建立了钢筋混凝土桥墩的弯剪数值分析模型,模型中以纤维模型模拟结构的弯曲变形和极限承载力,以MCFT理论计算桥墩的剪切变形,两者耦合共同考虑桥墩的弯剪作用。最终通过与6个弯剪破坏圆形截面桥墩拟静力试验结果的对比,验证了模型的准确性。
The vulnerabilities of reinforced concrete (RC) bridge columns toseismic actions have been repeatly demonstrated in recent events such as theLoma Prieta earthquake (1989), Northridge earthquake (1994), Kobeearthquake (1995), Chi-Chi earthquake (1999), and the Wenchuan earthquake(2008). The research on the seismic performance of RC bridge columns isimportant to ensure the seismic safety of RC bridges and crucial loads, andthe seismic ductility and energy absorption capacity of the RC bridgecolumns are key prerequisites of displacement/performance based seismicdesign of the bridges.
     Based on analysis of the collected seismic test results for RC bridgecolumns, quasi-static experimental research and numerical simulation, theseismic deformation capacity of solid and hollow bridge columns withnormal and high strength concrete and reinforcement was studied. Whichincluding the ductile deformability and drift based confining reinforcementof the bridge columns, the equivalent plastic hinge length for normal andhigh strength RC bridge columns, quasi-static experiment for thin-walledhollow bridge columns, the seismic deformability of hollow bridge columnsand the flexural-shear seismic analysis model for RC bridge columns. Themain work results and conclusion are summarized as follows:
     1. To study the seismic deformation capacity and confiningreinforcement for RC bridge columns,234quasi-static test results for solidRC bridge columns were collected, the code provisions for the amount ofconfining reinforcement in the potential plastic hinge region of the bridgecolumns were evaluated via comparing with the test results. The equation forthe deformability of the solid rectangular bridge columns was proposed basedon regression analysis of the collected test results. Then, design equations forconfining reinforcement required to achieve drift ratios of2%and3%of thebridge columns are suggested and verified.
     2. To assess the influence of using high strength reinforcement andconcrete on the equivalent plastic hinge length of the bridge columns,108testresults of the plastic hinge length for normal and high strength RC bridgecolumns were collected and analyzed, and the code provisions for the plastichinge length in and out of China were evaluated. The main influencing factorson the plastic hinge length of the bridge columns were discussed and a newequation for the plastic hinge length of RC bridge columns is proposed by regression analysis on the collected test results. It is concluded that theequivalent plastic hinge length mainly depending on the specimen length,section width in the loading direction and the diameter of longitudinalreinforcement.
     3. The application of hollow columns in large bridges in China wassummarized. Two same large-scale hollow RC pier specimens were designedand tested. One specimen was subject to displacement-controlled cyclic lateralloading with a constant axial load, and the other was subject todisplacement-controlled cyclic lateral loading with variable axial load.Behavior of the specimens were evaluated in terms of damage progress andfinal failure pattern, concrete cracking width, residual displacement and shearstrength. Test results revealed that both specimens exhibited a mixedflexure-shear damage mode firstly and exhibited stable hysteretic loops. Thedamage of the column including flexural and shear cracking, crushing of theconcrete, and buckling of the reinforcement. When the top displacementexceeding2%of the pier height, all the specimens collapsed suddenly due tolocal compression flange buckling, and the specimen under variable axial loadcollapsed more severely than the one under constant axial load.
     4. Based on the collected seismic test results for hollow bridge columns,the seismic deformability of the columns with flexure, flexure-shear and shearfailure modes were studied, the main influencing factors on the deformabilityof the columns were discussed and the code provisions were evaluated. It isfound that the deformation capacity of the hollow bridge piers will beincreased as the transverse reinforcement, longitudinal reinforcement, andweb width increasing, and decreased as the axial load ratio increasing. At last,design equations for confining reinforcement in the potential plastic hingeregion of hollow bridge columns are suggested based on the Caltrans seismicdesign code for bridges.
     5. A flexure-shear seismic analysis model for RC bridge columns wasproposed based on the fiber element model and the Modified CompressionField Theory (MCFT). In the seismic analysis model, the flexuraldeformation and the ultimate strength of the column were obtained by thefiber element model, while the shear deformation of the column was obtainedby the MCFT. The fiber model and the MCFT coupled to simulate theflexure-shear-axial interaction of the bridge piers. The accuracy of the modelis verified by comparing with quasi-static test results for6circular bridgecolumns with flexure-shear failure modes.
引文
[1]艾庆华,王东升,李宏男,孙治国.基于塑性铰模型的钢筋混凝土桥墩地震损伤评价[J].工程力学,2009,26(4):158-166.
    [2]崔海琴,贺拴海,宋一凡.空心矩形薄壁墩延性抗震性能试验[J].公路交通科技,2010,27(6):58-63.
    [3]崔海琴,贺拴海,赵小星,等.CFRP约束空心薄壁墩抗震性能试验[J].长安大学学报(自然科学版),2010,30(3):53-59.
    [4]杜修力,陈明琦,韩强.钢筋混凝土空心桥墩抗震性能试验研究[J].振动与冲击,2011,30(11):254-259.
    [5]杜修力,韩强,李忠献,等.5.12汶川地震中山区公路桥梁震害及启示[J].北京工业大学学报,2008,34(12):1270-1279.
    [6]范立础.桥梁抗震[M].上海:同济大学出版社,1997.
    [7]范立础,王君杰.桥梁抗震设计规范的现状与发展趋势[J].地震工程与工程振动,2001,21(2):70-77.
    [8]范云蕾,郭玉荣,肖岩.基于NetSLab远程协同试验平台的多跨桥梁抗震研究[J].自然灾害学报,2010,19(3):126-131.
    [9]郭磊,李建中,范立础.桥梁结构抗震设计中截面刚度的取值分析[J].同济大学学报(自然科学版),2004,32(11):1423-1427.
    [10]郝文秀,钟铁毅.活性粉末混凝土桥墩延性试验研究与数值分析[J].土木工程学报,2010,43(6):82-86.
    [11]黄建文,朱晞.近场地震作用下钢筋混凝土桥墩基于位移的抗震设计[J].土木工程学报,2005,38(4):84-90.
    [12]黄信,李忠献.动水压力作用对深水桥墩地震响应的影响[J].土木工程学报,2011,44(1):65-73.
    [13]鞠彦忠,阎贵平,刘林.低配筋大比例尺圆端型桥墩抗震性能的试验研究[J].土木工程学报,2003,36(11):65-69.
    [14]雷俊卿,宋力勋.汶川百花大桥震害分析与抗震性能研究[J].北京交通大学学报,2012,36(1):1-5.
    [15]李鸿晶,陆鸣,温增平,等.汶川地震桥梁震害的特征[J].南京工业大学学报(自然科学版),2009,31(1):24-29.
    [16]李志兴.高墩大跨混凝土刚构桥抗震性能研究[D].哈尔滨:中国地震局工程力学研究所,2010.
    [17]刘健新,张伟,张茜.洛河特大桥抗震性能计算[J].交通运输工程学报,2006,6(1):57-62.
    [18]刘林.高墩大跨铁路桥梁抗震设计与减震控制研究[D].北京:北京交通大学,2004.
    [19]刘鸣,陆本燕,刘伯权.钢筋混凝土桥墩破坏模式识别方法[J].中国公路学报,2011,24(3):58-63.
    [20]刘庆华,范立础.钢筋混凝土桥墩的延性分析[J].同济大学学报,1998,26(3):245-249.
    [21]刘艳辉,强士中.基于性能抗震设计的钢筋混凝土桥墩变形能力公式推倒及应用[J].公路交通科技,2009,26(3):94-99.
    [22]刘艳辉,赵世春,强士中.城市高架桥抗震性能水准的量化[J].西南交通大学学报,2010,45(1):54-58.
    [23]陆本燕,刘伯权,刘鸣,等.钢筋混凝土桥墩性能指标量化研究[J].中国公路学报,2010,23(6):49-57.
    [24]吕西林,周定松,蒋欢军.钢筋混凝土框架柱的变形能力及基于性能的抗震设计方法[J].地震工程与工程振动,2005,25(6):53-61.
    [25]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.
    [26]沈聚敏,瓮义军,冯世平.周期反复荷载下钢筋混凝土压弯构件的性能[J].土木工程学报,1982,3(2):53-64.
    [27]沈聚敏,刘竹青,翁义军.钢筋混凝土空心柱抗震性能的试验研究[J].建筑结构学报,1982,3(5):21-31.
    [28]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.
    [29]司炳君,孙治国,艾庆华,等.钢筋混凝土桥墩滞回性能的有限元参数敏感性分析及模型改进[J].工程力学,2009,26(1):174-180.
    [30]司炳君,孙治国,杜修力,等.钢筋混凝土桥墩地震弯剪破坏机理与震后快速修复技术研究[J].土木工程学报,2011,44(7):90-99.
    [31]司炳君,孙治国,任晓丹,等.钢筋混凝土桥墩滞回性能的有限元模拟分析[J].哈尔滨工业大学学报,2009,41(12):105-109.
    [32]司炳君,孙治国,王东升,等.高强箍筋约束高强混凝土柱抗震性能研究综述[J].土木工程学报,2009,42(4):1-9.
    [33]宋晓东.桥梁高墩延性抗震性能的理论与试验研究[D].上海:同济大学,2004.
    [34]孙利民,范立础.阪神地震后日本桥梁抗震设计规范的改订[J].同济大学学报,2001,29(1):60-64.
    [35]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.
    [36]孙治国,司炳君,王东升,等.高强箍筋高强混凝土柱约束箍筋用量研究[J].工程力学,2010,27(10):182-189.
    [37]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.
    [38]孙治国,王东升,郭迅,等.汶川大地震绵竹市回澜立交桥震害调查[J].地震工程与工程振动,2009,29(4):132-138.
    [39]孙治国,王东升,郭迅,等.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.
    [40]孙卓,李建中,阎贵平,等.钢筋混凝土单柱式桥墩抗震性能试验研究[J].同济大学学报(自然科学版),2006,34(2):160-164.
    [41]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.
    [42]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.
    [43]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.
    [44]王东升,孙治国,李晓莉,等.汶川大地震曲线梁桥震害及破坏机理分析[J].防灾减灾工程学报,2010,30(5):572-579.
    [45]王克海,李茜.高墩桥梁地震响应分析[J].世界桥梁,2006,(1):41-43.
    [46]王克海,林新元.徐水河大桥地震响应分析[J].世界桥梁,2004,(4):47-49.
    [47]魏标,李建中.基于位移的非规则梁桥抗震设计[J].土木工程学报,2011,44(8):95-101.
    [48]魏斌,李建中,蒋娜芳.考虑P-Δ效应的桥梁地震反应分析与设计[J].地震工程与工程振动,2010,30(3):129-135.
    [49]翁义军,沈聚敏,马宝民.复合箍对钢筋混凝土柱延性的改善[J].建筑结构学报,1985,6(1):41-47.
    [50]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.
    [51]薛瑞杰,袁万城.国内外桥梁延性抗震构造设计比较[J].工程抗震与加固改造,2009,31(2):1-8.
    [52]叶献国,王海波,孙利民,等.钢筋混凝土桥墩抗震耗能能力的试验研究[J].合肥工业大学学报(自然科学版),2005,28(9):1171-1177.
    [53]张昊之,刘伟庆,徐秀丽.基于性能的钢筋混凝土桥墩抗震变形能力的设计研究[J].建筑科学,2011,27(S1):12-16.
    [54]中华人民共和国交通部,JTG044—89,公路工程抗震设计规范[S].
    [55]中华人民共和国交通运输部,JTG/T B02-01—2008,公路桥梁抗震设计细则[S].
    [56]周艳,张雷明,刘西拉.美国Cypress高架桥地震倒塌的仿真分析[J].岩石力学与工程学报,2005,24(17):3035-3044.
    [57]庄卫林,刘振宇,蒋劲松.汶川大地震公路桥梁震害分析及对策[J].岩石力学与工程学报,2009,28(7):1377-1387.
    [58]周敉,王君杰,袁万城,等.基于精细有限元分析的猎德大桥抗震性能评价[J].同济大学学报(自然科学版),2008,36(2):143-148.
    [59]朱晞,江辉.桥梁墩柱基于性能的抗震设计方法[J].土木工程学报,2009,42(4):85-92.
    [60]卓卫东,范立础.延性桥墩塑性铰区最低约束箍筋用量[J].土木工程学报,2002,35(5):47-51.
    [61]宗周红,陈树辉,夏樟华.钢筋混凝土箱型高墩双向拟静力试验研究[J].防灾减灾工程学报,2010,30(4):369-374.
    [62] Priestley M J N.桥梁抗震设计与加固[M].袁万城等译.北京:人民交通出版社,1997.
    [63] AASHTO1996, Standard Specifications for Highway Bridges [S].
    [64] AASHTO LRFD2005, Bridge Design Specifications [S].
    [65] AASHTO-LRFD-2009, AASHTO Guide Specifications for LRFD Seismic BridgeDesign [S].
    [66] ACI318-08, Building Code Requirements for Structural Concrete and Commentar-y [S].
    [67] Bae S, Bayrak O. Seismic performance of full-scale reinforced concrete columns[J]. ACI Structural Journal,2008,105(2):123-133.
    [68] Bae S, Bayrak O. Plastic hinge length of reinforced concrete columns [J]. ACI Str-utural Journal,2008,105(3):290-300.
    [69] Bayrak O. Seismic performance of rectilinearly confined high strength concrete co-lumns [D]. Toronto: University of Toronto,1998.
    [70] Bentz E C. Sectional analysis of reinforced concrete members [D]. Toronto, Cana-da: University of Toronto,2000.
    [71] Bentz E C, Vecchio F J, Collins M P. Simplified modified compression field theoryfor calculating shear strength of reinforced concrete elements [J]. ACI Structural J-ournal,2006,103(4):614-623.
    [72] Berry M, Parrish M, Eberhard M. PEER Structural Performance Database, User’sManual [R]. Pacific Earthquake Engineering Research Center, University of Calif-ornia, Berkeley,2004.
    [73] BS EN1998-2:2005, Eurocode8-Design of Structures for Earthquake Resistance-Part2: Bridges [S].
    [74] Buckle I G, Goodson M, Cassano R, et al. Loma Prieta earthquake reconnaissancereport: bridge structures [J]. Earthquake Spectra,1990,6(S1):151-187.
    [75] Caltrans-2001, Seismic Design Criteria, Version1.2[S].
    [76] Caltrans-2006, Seismic design Criteria, Version1.4[S].
    [77] Calvi G M, Pavese A, Rasulo A, et al. Experimental and numerical studies on theseismic response of R.C. hollow bridge piers [J]. Bulletin of Earthquake Engineer-ing,2005,3(3):267-297.
    [78] Chai Y H, Priestley M J N, Seible F. Seismic retrofit of circular bridge columns forenhanced flexural performance [J]. ACI Structural Journal,1991,88(5):572-584.
    [79] Chang K C, Chang D W, Tsai M H, Sung Y C. Seismic performance of highwaybridges [J]. Earthquake Engineering and Engineering Seismology,2000,2(1):55-77.
    [80] Cheng C T, Mo Y L, Yeh Y K. Evaluation of as-built, retrofitted, and repairedshear-critical hollow bridge columns under earthquake-type loading [J]. Journal ofBridge Engineering, ASCE,2005,10(5):520-529.
    [81] Cheng C T, Yang J C, Yeh Y K, et al. Seismic performance of repaired hollow-bridge piers [J]. Construction and Building Materials,2003,17(5):339-351.
    [82] Delgado R, Delgado P, Poua N V, et al. Shear Effects on hollow section piers und-er seismic actions: Experimental and numerical analysis [J]. Bulletin of EarthquakeEngineering,2009,7(2):377-389.
    [83] Delgado P, Pouca N V, Arêde A, et al. Seismic retrofit of RC hollow-section pierswith shear failure [C]. IEM. Proceeding of the14th World Conference on Earthqu-ake Engineering, Beijing, China: China Earthquake Press,2008:1-8.
    [84] Esmaeily A, Xiao Y. Behavior of reinforced concrete columns under variable ax-al loads: Analysis [J]. ACI Structural Journal,2005,102(5):736-744.
    [85] Eurocode8-1998, Design Provisions for Earthquake Resistance of Structures-Part2: Bridges [S].
    [86] Faria R, Pouca N V, Delgado R. Simulation of the cyclic behaviour of R/C rectang-ular hollow section bridge piers via a detailed numerical model [J]. Journal of Eart-hquake Engineering,2004,8(5):725-748.
    [87] Fujino Y, Hashimoto S, Abe M. Damage analysis of hanshin expressway viaductsduring1995Kobe earthquake. I: Residual inclination of reinforced concrete piers[J]. Journal of Bridge Engineering, ASCE,2005,10(1):45-53.
    [88] Galeota D, Giammatteo M M, Marino R. Seismic resistance of high strength concr-ete columns [C]. N0.1390, Eleventh World Conference on Earthquake Engineering,Acapulco, Mexico,1996.
    [89] Gómez S R, akmak A, Shinozuka M. Damage analysis of simulated I-880struc-tures under the Loma Prieta earthquake [J]. Soil Dynamics and Earthquake Engine-ering,1995,14(4):313-319.
    [90] Guedes J, Pinto A V, Pegon P. Non-linear shear model for R/C piers [R]. Joint Re-search Center, ELSA Unit, Ispra, Italy,2010.
    [91] Ho J C M. Inelastic design of reinforced concrete beams and limited ductile high-strength concrete columns [D]. Hong Kong: The University of Hong Kong,2003.
    [92] Hose Y D. Seismic performance and failure behavior of plastic hinge regions inflexural bridge columns [D]. San Diego: University of California, San Diego,2001.
    [93] Hoshikuma J I, Priestley M J N. Flexural behavior of circular hollow columnswith a single layer of reinforcement under seismic loading [R]. Department of Str-uctural Engineering, University of California, San Diego,2000.
    [94] Hoshikuma J, Unjoh S, Nagaya K. Flexural ductility of full-scale RC bridge colu-mns subjected to cyclic loading [C]. Proceeding of first fib congress, Osaka,2002.
    [95] Housner G W, Thiel C C. Competing against time: report of the governor’s boardof inquiry on the1989Loma Prieta earthquake [J]. Earthquake Spectra,1990,6(4):681-711.
    [96] Hwang S K, Yun H D. Effects of transverse reinforcement on flexural behaviour ofhigh-strength concrete columns [J]. Engineering Structures,2004,26(1):1-12.
    [97] Hsu Y T, Fu C C. Study of damaged Wushi bridge in Taiwan earthquake [J]. Pract-ice Periodical on Structural Design and Construction, ASCE,2000,5(4):166-171.
    [98] Isakovi T, Bevc J, Fischinger M. Modeling the cyclic flexural and shear responseof the R. C. hollow box columns of an existing viaduct [J]. Journal of EarthquakeEngineering,2008,12(7):1120-1138.
    [99] Jaradat O A, Mclean D I, Marsh M L. Performance of existing bridge columns und-er cyclic loading—Part1: Experimental results and observed behavior [J]. ACI Str-uctural Journal,1998,95(6):695-704.
    [100] Jaradat O A, Mclean D I, Marsh M L. Performance of existing bridge columns un-der cyclic loading—Part2: Analysis and comparisons with theory [J]. ACI Struct-ural Journal,1999,96(1):57-67.
    [101] Kawashima K. Damage of bridges resulting from fault rupture in the1999Kocaeliand Duzce, Turkey earthquakes and the1999Chi-Chi, Taiwan earthquake [R]. To-kyo: Tokyo Institute of Technology,2001.
    [102] Kawashima K, Une H, Sakai J. Seismic performance of hollow reinforced concretearch ribs subjected to cyclic lateral force under varying axial load [J]. Journal ofStructural Engineering, JSCE,2002,48A(2):747-757.
    [103] Kawashima K, Unjoh S. Impact of Hanshin/Awaji earqhauek on seismic design andseismic strengthening of highway bridges [R]. Tokyo: Tokyo Institute of Technol-ogy,1995.
    [104] Kenmotsu Y, Kawashima K. Seismic performance of hollow reinforced concretecolumns with densely confined zones [J]. Proceeding of Japan Society of Civil En-gineers,2001,682:57-69.
    [105] Kunnath S K, Gross J L. Inelastic response of the Cypress viaduct to the Loma Pri-eta earthquake [J]. Engineering Structures,1995,17(7):485-493.
    [106] Lampropoulos A P, Dritsos S E. Modeling of RC columns strengthened with RCjackets [J]. Earthquake Engineering and Structural Dynamics,2011,40(14):1-17.
    [107] Lee D H, Choi E, Zi G. Evaluation of earthquake deformation and performance forRC bridge piers [J]. Engineering Structures,2005,27(10):1451-1464.
    [108] Lee D H, Elnashai A S. Seismic analysis of RC bridge columns with flexure-shearinteraction [J]. Journal of Structural Engineering, ASCE,2001,127(5):546-553.
    [109] Lee D H, Elnashai A S. Inelastic seismic analysis of RC bridge piers includingflexure-shear-axial interaction [J]. Structural Engineering and Mechanics,2002,13(3):241-260.
    [110] Légeron F, Paultre P. Behavior of high-strength concrete columns under cyclicflexure and constant axial load [J]. ACI Structural Journal,2000,97(4):591-601.
    [111] Lehman D E. Seismic performance of well-confined concrete bridge columns [D].Berkeley: University of California, Berkeley,1998.
    [112] Lehman D, Moehle J, Mahin S, et al. Experimental evaluation of the seismic perfo-rmance of reinforced concrete bridge columns [J]. Journal of Structural Engineeri-ng, ASCE,2004,130(6):869-879.
    [113] Li B, Park R. Confining reinforcement for high-strength concrete columns [J]. ACIStructural Journal,2004,101(3):314-324.
    [114] Li Jianzhong, Peng Tianbo, Xu Yan. Damage investigation of girder bridges underthe Wenchuan earthquake and corresponding seismic design recommendations [J].Earthquake Engineering and Engineering Vibration,2008,7(4):337-344.
    [115] Lipien W. Behavior of square high strength concrete columns under load reversals[D]. Ottawa, Ontario: University of Ottawa,1995.
    [116] Mander J B. Seismic design of bridge piers [D]. Christchurch, New Zealand:University of Canterbury,1983.
    [117] Menegotto M, Pinto P E. Method of analysis for cyclically loaded reinforcedconcrete plane frames including changes in geometry and nonelastic behavior ofelements under combined normal force and bending [R]. IABSE PreliminaryReport for Symposium on Resistance and Ultimate Deformability of StructuresActed on by Well-Defined Repeated Loads, Lisbon, Portugal,1973.
    [118] Miranda E, Bertero V V. Evaluation of the failure of the cypress viaduct in theLoma Prieta earthquake [J]. Bulletin of the Seismological Society of America,1991,81(5):2070-2086.
    [119] Mo Y L, Jeng C H, Perng S F. Seismic shear behavior of rectangular hollow bridgecolumns [J]. Structural Engineering and Mechanics,2001,12(4):429-448.
    [120] Mo Y L, Nien I C. Seismic performance of hollow high-strength concrete bridgecolumns [J]. Journal of Bridge engineering, ASCE,2002,7(6):338-349.
    [121] Mo Y L, Wong D C, Maekawa K. Seismic performance of hollow bridge columns[J]. ACI Structural Journal,2003,100(3):337-348.
    [122] Mo Y L, Yeh Y K, Cheng C T, et al. Seismic performance and retrofit of hollowbridge columns [J]. Earthquake Engineering and Engineering Seismology,2001,3(1):59-66.
    [123] Mo Y L, Yeh Y K, Hsieh D M. Seismic retrofit of hollow rectangular bridge colu-mns [J]. Journal of Composites for Construction, ASCE,2004,8(1):43-51.
    [124] Moehle J, Fenves G, Mayes R, et al. Highway bridges and traffic management [J].Earthquake Spectra,1995,11(S2):287-372.
    [125] Mostafaei H, Kabeyasawa T. Axial-shear-flexure interaction approach for reinforc-ed concrete columns [J]. ACI Structural Journal,2007,104(2):218-226.
    [126] Mostafaei H, Vecchio F J. Uniaxial shear-flexure model for reinforced concreteelements [J]. Journal of Structural Engineering, ASCE,2008,134(9):1538-1547.
    [127] Mostafaei H, Vecchio F J, Kabeyasawa T. Deformation capacity of reinforcedconcrete columns [J]. ACI Structural Journal,2009,106(2):187-195.
    [128] Mzrtinez-Rueda J E, Elnashai A S. Confined concrete model under cyclic load [J].Materials and Structures,1997,30(3):139-147.
    [129] NZS3101:1995, Code of Practice for Design of Concrete Structures [S].
    [130] Ogata T, Suda K, Masukawa J. Transverse reinforcement and ductility of reinforc-ed concrete high pier with hollow section [C].12WCEE. Proceeding of the12thWorld Conference on Earthquake Engineering, Auckland, New Zealand:12WCEEPublications,2000:1-8.
    [131] Ohuchi H, Matsuda T, Goto Y. A study on the Cypress viaduct collapse and seism-ic performance of a retrofitted bent [J]. Structural Engineering&Earthquake Engi-neering, JSCE,1992,9(1):65-76.
    [132] Ozcebe G, Saatcioglu M. Hysteretic shear model for reinforced concrete members[J]. Journal of Structural Engineering, ASCE,1989,115(1):132-148.
    [133] Park R, Priestley M J N, Gill W D. Ductility of square-confined concrete columns[J]. Journal of the Structural Division, ASCE,1982,108(4):929-951.
    [134] Paulay T, Priestley M J N. Seismic design of reinforced concrete and masonry bui-ldings [M]. New York: John Wiley and Sons,1992.
    [135] Paultre P, Eid R, Robles H I, et al. Seismic performance of circular high-strengthconcrete columns [J]. ACI Structural Journal,2009,106(4):395-404.
    [136] Paultre P, Légeron F, Mongeau D. Influence of concrete strength and transversereinforcement yield strength on behavior of high-strength concrete columns [J].ACI Structural Journal,2001,98(4):490-501.
    [137] Pinto A V, Molina J, Tsionis G. Cyclic Tests on large-scale models of existing bri-dge piers with rectangular hollow cross-section [J]. Earthquake Engineering andStructural Dynamics,2003,32(13):1995-2012.
    [138] Pinto A V, Verzeletti G, Magonette G, et al. Pseudo-dynamic testing of large-scaleR/C bridges in ELSA [C]. Elsevier Science Ltd. Proceeding of the the11th WorldConference on Earthquake Engineering. Acapulco, Mexico: Elsevier Science Ltd,1996:1-8.
    [139] Priestley M J N, Park R, Potangaroa R T. Ductility of spirally-confined concretecolumns [J]. Journal of the Structural Division, ASCE,1981,107(1):181-202.
    [140] Priestley M J N, Park R. Strength and ductility of concrete bridge columns underseismic loading [J]. ACI Structural Journal,1987,84(1):61-76.
    [141] Ranzo G, Priestley M J N. Seismic performance of large RC circular hollow colu-mns [C].12WCEE. Proceeding of the12th World Conference on Earthquake Eng-ineering, Auckland, New Zealand:12WCEE Publications,2000:1-8.
    [142] Ruangrassamee A, Kawashima K. Control of nonlinear bridge response with poun-ding effect by variable dampers [J]. Engineering Structures,2003,25(5):593-606.
    [143] Saatcioglu M, Baingo D. Circular high-strength concrete columns under simulatedseismic loading [J]. Journal of Structural Engineering, ASCE,1999,125(3):272-280.
    [144] Saatcioglu M, Razvi S R. Displacement-based design of reinforced concrete colu-mns for confinement [J]. ACI Structural Journal,2002,99(1):3-11.
    [145] Sakai K, Sheikh S A. What do we know about confinement in reinforced concretecolumns (A critical review of previous work and code provisions)[J].ACI Structu-ral Journal,1989,86(2):192-207.
    [146] Setzler E J, Sezen H. Model for the lateral behavior of reinforced concrete columnsincluding shear deformations [J]. Earthquake Spectra,2008,24(2):493-511.
    [147] Sezen H, Chowdhury T. Hysteretic model for reinforced concrete columns includi-ng the effect of shear and axial load failure [J]. Journal of Structural Engineering,ASCE,2009,135(2):139-146.
    [148] Sezen H, Moehle J P. Seismic tests of concrete columns with light transverse rein-forcement [J]. ACI Structural Journal,2006,103(6):842-849.
    [149] Sheikh M N, Vivier A, Legeron F. Seismic assessment of hollow core concrete br-idge piers [C]. Ninth Canadian Conference on Earthquake Engineering, Ottawa,Canada, June2007.
    [150] Sheikh S A, Khoury S S. Confined concrete columns with stubs [J]. ACI StructuralJournal,1993,90(4):414-431.
    [151] Sheikh S A, Shah D V, Khoury S S. Confinement of high-strength concrete colum-ns [J]. ACI Structural Journal,1994,91(1):100-111.
    [152] Spacone E, Filippou F, Taucer F F. Fiber beam-column model for non-linear anal-ysis of R/C frames: Part I. Formulation [J]. Earthquake Engineering and StructuralDynamics,1996,25(7):711-725.
    [153] Spacone E, Filippou F, Taucer F F. Fiber beam-column model for non-linear anal-ysis of R/C Frames: Part II. Applications [J]. Earthquake Engineering and Structu-ral Dynamics,1996,25(7):727-742.
    [154] Sun Zhiguo, Si Bingjun, Wang Dongsheng, Guo Xun. Experimental research andfinite element analysis of bridge piers failed in flexure-shear modes [J]. Earthqua-ke Engineering and Engineering Vibration,2008,7(4):403-414.
    [155] Takahashi Y, Iemura H. Inelastic seismic performance of RC tall piers with hollowsection [C].12WCEE. Proceeding of the12th World Conference on EarthquakeEngineering, Auckland, New Zealand:12WCEE Publications,2000:1-8.
    [156] Tanaka H. Effect of lateral confining reinforcement on the ductile behavior of rei-nforced concrete columns [D]. Christchurch, New Zealand: University of Canterb-ury,1990.
    [157] Taylor A W, Rowell R B, Breen J E. Behavior of thin-walled concrete box piers[J]. ACI Structural Journal,1995,92(3):319-333.
    [158] Telemachos B P, Michael N F. Deformations of Reinforced Concrete Members atYielding and Ultimate [J]. ACI Structural Journal,2001,98(2):135-148.
    [159] Tsuno K, Park R. Experimental study of reinforced concrete bridge piers subjectedto bi-directional quasi-static loading [J]. Structural Engineering/Earthquake Engi-neering, JSCE,2004,21(1):11-26.
    [160] Vecchio F J, Collins M P. The modified compression-field theory for reinforcedconcrete elements subjected to shear [J]. ACI Structural Journal,1986,83(2):219-231.
    [161] Watson S, Zahn F A, Park R. Confining reinforcement for concrete columns [J].Journal of Structural Engineering, ASCE,1994,120(6):1798-1824.
    [162] Watson S, Park R. Simulated seismic load tests on reinforced concrete columns [J].Journal of Structural Engineering, ASCE,1994,120(6):1825-1848.
    [163] Xiong Zhaohui. Reinforced concrete column behavior under cyclic loading [D].Hong Kong: The University of Hong Kong,2001.
    [164] Xu S Y, Zhang J. Hysteretic shear-flexure interaction model of reinforced concretecolumns for seismic response assessment of bridges [J]. Earthquake Engineeringand Structural Dynamics,2011,40(3):315-337.
    [165] Yashinsky M. Performance of bridge seismic retrofits during Northridge earthqua-ke [J]. Journal of Bridge Engineering, ASCE,1998,3(1):1-14.
    [166] Yeh Y K, Mo Y L, Yang C Y. Seismic performance of hollow circular bridge piers[J]. ACI Structural Journal,2001,98(6):862-871.
    [167] Yeh Y K, Mo Y L, Yang C Y. Seismic performance of rectangular hollow bridgecolumns [J]. Journal of Structural Engineering, ASCE,2002,128(1):60-68.
    [168] Yeh Y K, Mo Y L, Yang C Y. Full-scale tests on rectangular hollow bridge piers[J]. Materials and Structures,2002,35(2):117-125.
    [169] Yun H W. Full-scale experimental and analytical studies on high-strength concretecolumns [D]. Los Angeles, California: University of Southern California,2003.
    [170] Zahn F A. Design of reinforced concrete bridge columns for strength and ductility
    [D]. Christchurch, New Zealand: University of Canterbury,1985.
    [171] Zahn F A, Park R, Priestley M J N. Flexural strength and ductility of circular holl-ow reinforced concrete columns without confinement on inside face [J]. ACI Stru-ctural Journal,1990,87(2):156-166.
    [172] Zatar W A, Mutsuyoshi H. Residual displacements of concrete bridge piers subjec-ted to near field earthquakes [J]. ACI Structural Journal,2002,99(6):740-749.
    [173] Zatar W A, Mutsuyoshi H. Reduced residual displacements of partially prestressedconcrete bridge piers [C]//Proceeding of the12th World Conference on Earthqua-ke Engineering. Auckland, New Zealand,2000:1-8.