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Article(id=1241791681293517040, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241791680479822062, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2025.0211, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1729526400000, receivedDateStr=2024-10-22, revisedDate=1733328000000, revisedDateStr=2024-12-05, acceptedDate=null, acceptedDateStr=null, onlineDate=1773995808193, onlineDateStr=2026-03-20, pubDate=1745424000000, pubDateStr=2025-04-24, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773995808193, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773995808193, creator=13701087609, updateTime=1773995808193, updator=13701087609, issue=Issue{id=1241791680479822062, tenantId=1146029695717560320, journalId=1241701559352995854, year='2025', volume='45', issue='2', pageStart='1', pageEnd='237', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773995807999, creator=13701087609, updateTime=1773996976041, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241796579670163949, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241791680479822062, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241796579670163950, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241791680479822062, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=118, endPage=126, ext={EN=ArticleExt(id=1241791683747184899, articleId=1241791681293517040, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Seismic response mitigation of long-span continuous rigid-frame bridges with high piers based on TMDI, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The fixed connection between the piers and the superstructure of rigid-frame bridges with high piers exhibits limitations in seismic design. Cracking of the cross-section and prestressing tendon stress loss can be found in the main girder subjected to seismic loads. The inertialr system ( i. e. tuned mass-damper-inerter, TMDI) contains an inertial container and a traditional tuned mass damper (TMD). It is a new method for structural seismic control in recent years. This study focuses a high-pier, long-span continuous rigid-frame bridge, considering the construction process and combining Midas Civil and the OpenSees to establish a nonlinear seismic response numerical model. Using 10 near-fault pulse-like ground motion records as input, this study investigates the seismic control behavior of a distributed configuration of multiple TMDIs. The results show that when the ground motion excites the bridge along the longitudinal direction, TMDIs can effectively prevent the cracking of the top and bottom slabs of the main girder, although the internal forces of the web of the main girder increase slightly. When the ground motion excites the bridge along the transverse direction, TMDIs significantly reduce the internal forces on the web of the main span. When ground motions are input in both horizontal directions, TMDIs can effectively mitigate the stress on the top slab, bottom slab, and web of the main span. Regarding the pier response, the average seismic reduction proportions of the maximum displacement at the pier top are 52% in the longitudinal direction and 21% in the transverse direction, respectively. The seismic reduction proportions of the maximum bending moment in the longitudinal direction is 31%. Although TMDIs increase the bottom bending moment of the pier by approximately 10% in the transverse direction, they effectively control the residual displacement of the bridge pier.

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高墩大跨连续刚构桥因主墩与上部结构固结，其减震控制设计存在一定的局限性，且主梁因地震作用会存在截面开裂及预应力束应力损失等现象。惯容系统是近年发展的结构减震控制新方式，特别是将惯容器与传统调谐质量阻尼器（tuned mass damper，TMD）结合，形成的调谐质量惯容阻尼器（tuned mass-damper-inerter，TMDI）。文中以某高墩大跨连续刚构桥为例，考虑施工过程结合Midas Civil与OpenSees软件建立非线性地震反应分析模型，以10条近断层脉冲波为输入，研究了分布式设置（多个）TMDI对其地震反应的控制效果。研究结果表明：地震动沿纵桥向输入时，TMDI可有效避免主梁顶板、底板开裂，但主梁腹板受力略有增大；沿横桥向输入时，TMDI则会明显降低主跨腹板受力；当地震动双向水平输入时，TMDI无论对主梁顶板、底板，还是主跨腹板的应力都有很好的减轻作用。在桥墩反应方面，墩顶最大位移平均减震率为52%（纵桥向）和21%（横桥向），纵桥向最大弯矩减震率是31%，在横桥向TMDI虽然会放大约10%的墩底弯矩，但它可控制桥墩的（弹塑性）残余位移反应。

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王东升（1974—），男，教授，博士，主要从事地震工程研究。E-mail：
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代建成（1995—），男，博士研究生，主要从事地震工程研究。E-mail：

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代建成（1995—），男，博士研究生，主要从事地震工程研究。E-mail：

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代建成（1995—），男，博士研究生，主要从事地震工程研究。E-mail：

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IEEE Transactions on Automatic Control, 2002, 47(10): 1648-1662., articleTitle=Synthesis of mechanical networks: The inerter, refAbstract=null), Reference(id=1241802918119150433, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, doi=null, pmid=null, pmcid=null, year=2023, volume=44, issue=3, pageStart=11, pageEnd=19, url=null, language=null, rfNumber=[20], rfOrder=28, authorNames=康建飞, 薛松涛, 谢丽宇, journalName=建筑结构学报, refType=null, unstructuredReference=康建飞，薛松涛，谢丽宇. 双向地震作用下拉索支撑惯容系统及其在钢结构中的应用[J]. 建筑结构学报, 2023, 44(3): 11-19., articleTitle=双向地震作用下拉索支撑惯容系统及其在钢结构中的应用, refAbstract=null), Reference(id=1241802918274339699, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, doi=null, pmid=null, pmcid=null, year=2023, volume=44, issue=3, pageStart=11, pageEnd=19, url=null, language=null, rfNumber=[20], rfOrder=29, authorNames=KANG Jianfei, XUE Songtao, XIE Liyu, journalName=Journal of Building Structures, refType=null, unstructuredReference=KANG Jianfei, XUE Songtao, XIE Liyu. Cable-bracing inerter system and its application in steel structure subjected to bi-directional ground motions[J]. Journal of Building Structures, 2023, 44(3): 11-19. (in Chinese), articleTitle=Cable-bracing inerter system and its application in steel structure subjected to bi-directional ground motions, refAbstract=null), Reference(id=1241802918408557441, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, doi=null, pmid=null, pmcid=null, year=2022, volume=42, issue=6, pageStart=104, pageEnd=113, url=null, language=null, rfNumber=[21], rfOrder=30, authorNames=谢丽宇, 班鑫磊, 康建飞, journalName=地震工程与工程振动, refType=null, unstructuredReference=谢丽宇，班鑫磊，康建飞，等.基于模态参与消减的直连拉索连接惯容系统的简易算法[J].地震工程与工程振动, 2022, 42(6): 104-113., articleTitle=基于模态参与消减的直连拉索连接惯容系统的简易算法, refAbstract=null), Reference(id=1241802918622466961, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, doi=null, pmid=null, pmcid=null, year=2022, volume=42, issue=6, pageStart=104, pageEnd=113, url=null, language=null, rfNumber=[21], rfOrder=31, authorNames=XIE Liyu, BAN Xinlei, KANG Jianfei, journalName=Earthquake Engineering and Engineering Dynamics, refType=null, unstructuredReference=XIE Liyu, BAN Xinlei, KANG Jianfei, et al. Study on a simple design method for direct connected cable inerter system based on modal participation cancellation[J]. Earthquake Engineering and Engineering Dynamics, 2022, 42(6): 104-113. (in Chinese), articleTitle=Study on a simple design method for direct connected cable inerter system based on modal participation cancellation, refAbstract=null), Reference(id=1241802918836376483, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, doi=null, pmid=null, pmcid=null, year=2020, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[22], rfOrder=32, authorNames=童磊, journalName=null, refType=null, unstructuredReference=童磊. 汶川地震庙子坪特大桥主桥震害分析[D]. 天津：河北工业大学，2020., articleTitle=汶川地震庙子坪特大桥主桥震害分析, refAbstract=null), Reference(id=1241802918949622705, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, doi=null, pmid=null, pmcid=null, year=2020, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[22], rfOrder=33, authorNames=TONG Lei, journalName=null, refType=null, unstructuredReference=TONG Lei. Seismic damage analysis of the main bridge of Miaoziping bridge in Wenchuan earthquake[D]. Tianjin: Hebei University of Technology, 2020. (in Chinese), articleTitle=Seismic damage analysis of the main bridge of Miaoziping bridge in Wenchuan earthquake, refAbstract=null)], funds=[Fund(id=1241802912742052291, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, awardId=52178473, language=CN, fundingSource=国家自然科学基金项目(52178473), fundOrder=null, country=null), Fund(id=1241802912846909902, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, awardId=2020B1212060071, language=CN, fundingSource=广东省地震工程与应用技术重点实验室开放基金项目(2020B1212060071), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1241802897101492679, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, xref=1., ext=[AuthorCompanyExt(id=1241802897114075592, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, companyId=1241802897101492679, language=EN, country=null, province=null, city=null, postcode=null, 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tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Fig. 1, caption=Long-span continuous rigid frame bridge with high piers, figureFileSmall=3pHCsnAyVXVWU7g4BcRfcA==, figureFileBig=qkqFw73mDmEF4uxAhUe+sA==, tableContent=null), ArticleFig(id=1241802904886121380, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=图1, caption=高墩大跨连续刚构桥, figureFileSmall=3pHCsnAyVXVWU7g4BcRfcA==, figureFileBig=qkqFw73mDmEF4uxAhUe+sA==, tableContent=null), ArticleFig(id=1241802905024533430, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Fig. 2, caption=Bridge nonlinear seismic response analysis model by OpenSees, figureFileSmall=sk3LvH7iqp+RSstmvlFEIA==, figureFileBig=m+BNOrW6qHCIfvamV+Z8/Q==, tableContent=null), ArticleFig(id=1241802905141973955, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=图2, caption=OpenSees桥梁非线性地震反应分析模型, figureFileSmall=sk3LvH7iqp+RSstmvlFEIA==, figureFileBig=m+BNOrW6qHCIfvamV+Z8/Q==, tableContent=null), ArticleFig(id=1241802905297163215, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Fig. 3, caption=Layout diagram of TMDI, figureFileSmall=KlqPYThY3VWylkwnYIpbNg==, figureFileBig=2l4fWzP2thFLA5qNxx7Sbg==, tableContent=null), ArticleFig(id=1241802905410409433, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=图3, caption=TMDI布置图, figureFileSmall=KlqPYThY3VWylkwnYIpbNg==, figureFileBig=2l4fWzP2thFLA5qNxx7Sbg==, tableContent=null), ArticleFig(id=1241802905515267043, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Fig. 4, caption=Stress response of the main girder under longitudinal bridge direction input, figureFileSmall=+lt/vStgHK9O9Iv1H1OUEg==, figureFileBig=O8sLXjpo+bzv15byJ+APtA==, tableContent=null), ArticleFig(id=1241802905657873397, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=图4, caption=主梁应力反应（纵桥向输入）, figureFileSmall=+lt/vStgHK9O9Iv1H1OUEg==, figureFileBig=O8sLXjpo+bzv15byJ+APtA==, tableContent=null), ArticleFig(id=1241802905817255941, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Fig. 5, caption=Bending moment response of bridge piers under longitudinal bridge direction input, figureFileSmall=B+sC4KPJmheaNBundK7vrw==, figureFileBig=hBCYA+ldec7mj4995xJo/A==, tableContent=null), ArticleFig(id=1241802905922113555, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=图5, caption=桥墩墩身弯矩反应（纵桥向输入）, figureFileSmall=B+sC4KPJmheaNBundK7vrw==, figureFileBig=hBCYA+ldec7mj4995xJo/A==, tableContent=null), 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label=Fig. 9, caption=Time history of pier displacement under transverse bridge input, figureFileSmall=w673+H9DDRy0kILOOPrL+A==, figureFileBig=lf4fPsGXKcP2qf0pEEM3Og==, tableContent=null), ArticleFig(id=1241802908539359373, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=图9, caption=桥墩位移时程反应（横桥向输入）, figureFileSmall=w673+H9DDRy0kILOOPrL+A==, figureFileBig=lf4fPsGXKcP2qf0pEEM3Og==, tableContent=null), ArticleFig(id=1241802908681965722, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Fig. 10, caption=Stress response of main girder under bidirectional input, figureFileSmall=658ztw6uxISLxRTongpnFg==, figureFileBig=IEZtBP5KSA9RMncX2DxYJw==, tableContent=null), ArticleFig(id=1241802908837154986, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=图10, caption=主梁应力反应（双向输入）, figureFileSmall=658ztw6uxISLxRTongpnFg==, figureFileBig=IEZtBP5KSA9RMncX2DxYJw==, tableContent=null), ArticleFig(id=1241802908962984118, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Fig. 11, caption=Relative displacement response of mass blocks in the longitudinal direction of bridges, figureFileSmall=pRrfgL83HWTnO7/uq+qqmA==, figureFileBig=jxv+i0VH/q9AZZAVnUAFDQ==, tableContent=null), ArticleFig(id=1241802909130756292, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=图11, caption=TMDI质量块相对位移反应（纵桥向输入）, figureFileSmall=pRrfgL83HWTnO7/uq+qqmA==, figureFileBig=jxv+i0VH/q9AZZAVnUAFDQ==, tableContent=null), ArticleFig(id=1241802909281751254, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Fig. 12, caption=Relative displacement response of mass blocks in the transversal direction of bridges, figureFileSmall=ErwdjsMiAjmiGmR3Kg4Prw==, figureFileBig=rxI35cRArpDqn7kA7L5Lzg==, tableContent=null), ArticleFig(id=1241802909499855083, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=图12, caption=TMDI质量块相对位移反应（横桥向输入）, figureFileSmall=ErwdjsMiAjmiGmR3Kg4Prw==, figureFileBig=rxI35cRArpDqn7kA7L5Lzg==, tableContent=null), ArticleFig(id=1241802909659238656, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Table 1, caption=

Near-fault ground motion records

, figureFileSmall=null, figureFileBig=null, tableContent=
编号地震事件年份台站震级MW断层距/km
1Imperial Valley-061979El Centro Array #76.530.56
2Loma Prieta1989Saratoga-Aloha Ave6.938.50
3Erzican1992Erzincan6.694.38
4Landers1992Lucerne7.282.19
5Kocaeli1999Izmit7.517.21
6Chi-Chi1999TCU0527.620.70
7Chi-Chi1999TCU0547.625.30
8Chi-Chi1999TCU0657.620.57
9Chi-Chi1999TCU1027.621.49
10Duzce1999Duzce7.146.58
), ArticleFig(id=1241802909797650709, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=表1, caption=

近断层地震动记录

, figureFileSmall=null, figureFileBig=null, tableContent=
编号地震事件年份台站震级MW断层距/km
1Imperial Valley-061979El Centro Array #76.530.56
2Loma Prieta1989Saratoga-Aloha Ave6.938.50
3Erzican1992Erzincan6.694.38
4Landers1992Lucerne7.282.19
5Kocaeli1999Izmit7.517.21
6Chi-Chi1999TCU0527.620.70
7Chi-Chi1999TCU0547.625.30
8Chi-Chi1999TCU0657.620.57
9Chi-Chi1999TCU1027.621.49
10Duzce1999Duzce7.146.58
), ArticleFig(id=1241802909940257062, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Table 2, caption=

Bending moment response at the top of the bridge pier under longitudinal bridge direction input

, figureFileSmall=null, figureFileBig=null, tableContent=
地震动编号墩顶最大弯矩
无控制/（×103 kN•m）TMDI控制/（×103 kN•m）减震率/%
11694769-54.60
21327673-49.28
32853883-69.05
441165058.15
5945641-32.17
627182299-15.42
725681288-49.84
862675019.81
930401538-49.41
101492762-48.93
均值17671025-41.99
), ArticleFig(id=1241802910112223541, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=表2, caption=

墩顶弯矩反应（纵桥向输入）

, figureFileSmall=null, figureFileBig=null, tableContent=
地震动编号墩顶最大弯矩
无控制/（×103 kN•m）TMDI控制/（×103 kN•m）减震率/%
11694769-54.60
21327673-49.28
32853883-69.05
441165058.15
5945641-32.17
627182299-15.42
725681288-49.84
862675019.81
930401538-49.41
101492762-48.93
均值17671025-41.99
), ArticleFig(id=1241802910229664069, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Table 3, caption=

Bending moment response at the bottom of the bridge pier under longitudinal bridge direction input

, figureFileSmall=null, figureFileBig=null, tableContent=
地震动编号墩底最大弯矩
无控制/（×103 kN•m）TMDI控制/（×103 kN•m）减震率/%
125771337-48.12
222741351-40.59
339271828-53.45
4642124794.24
520571277-37.92
636102815-22.02
731732275-28.30
8949122328.87
934452598-24.59
1025471402-44.95
均值25201735-31.14
), ArticleFig(id=1241802910363881813, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=表3, caption=

墩底弯矩反应控制（纵桥向输入）

, figureFileSmall=null, figureFileBig=null, tableContent=
地震动编号墩底最大弯矩
无控制/（×103 kN•m）TMDI控制/（×103 kN•m）减震率/%
125771337-48.12
222741351-40.59
339271828-53.45
4642124794.24
520571277-37.92
636102815-22.02
731732275-28.30
8949122328.87
934452598-24.59
1025471402-44.95
均值25201735-31.14
), ArticleFig(id=1241802910510682467, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Table 4, caption=

Maximum displacement at the top of the main pier under longitudinal bridge direction input

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地震动编号墩顶最大位移地震动编号墩顶最大位移
无控制/cmTMDI控制/cm减震率/%无控制/cmTMDI控制/cm减震率/%
130.0211.77-60.79753.8220.49-61.93
217.189.80-42.9686.7311.3368.35
354.2913.59-74.97975.9625.15-66.89
44.779.3395.601022.9311.33-50.59
515.949.82-38.39
666.7443.85-34.30均值34.8416.65-52.22
), ArticleFig(id=1241802910594568556, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=表4, caption=

主墩墩顶位移反应（纵桥向输入）

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地震动编号墩顶最大位移地震动编号墩顶最大位移
无控制/cmTMDI控制/cm减震率/%无控制/cmTMDI控制/cm减震率/%
130.0211.77-60.79753.8220.49-61.93
217.189.80-42.9686.7311.3368.35
354.2913.59-74.97975.9625.15-66.89
44.779.3395.601022.9311.33-50.59
515.949.82-38.39
666.7443.85-34.30均值34.8416.65-52.22
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Bending moment response at the bottom of the bridge pier under transverse bridge input

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地震动编号墩底最大弯矩地震动编号墩底最大弯矩
无控制/（×103 kN•m）TMDI控制/（×103 kN•m）减震率/%无控制/（×103 kN•m）TMDI控制/（×103 kN•m）减震率/%
134992730-21.98740323776-6.35
21318790-40.0685032591415.11
323941613-32.6293053359817.85
430046555.001029062329-19.86
510212287124.00
63094418635.29均值2212243710.15
), ArticleFig(id=1241802910846226831, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=表5, caption=

墩底弯矩反应（横桥向输入）

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地震动编号墩底最大弯矩地震动编号墩底最大弯矩
无控制/（×103 kN•m）TMDI控制/（×103 kN•m）减震率/%无控制/（×103 kN•m）TMDI控制/（×103 kN•m）减震率/%
134992730-21.98740323776-6.35
21318790-40.0685032591415.11
323941613-32.6293053359817.85
430046555.001029062329-19.86
510212287124.00
63094418635.29均值2212243710.15
), ArticleFig(id=1241802910972055966, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=EN, label=Table 6, caption=

Maximum displacement at the top of the main pier under transverse bridge input

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地震动编号墩顶最大位移地震动编号墩顶最大位移
无控制/cmTMDI控制/cm减震率/%无控制/cmTMDI控制/cm减震率/%
167.8735.08-48.317221.96107.73-51.46
214.458.63-40.2884.5335.09674.61
333.6217.40-48.259148.7168.71-53.80
42.774.9578.701039.4626.36-33.20
59.8425.99164.13
6152.38222.3545.92均值695.59552.29-20.60
), ArticleFig(id=1241802911093690797, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791681293517040, language=CN, label=表6, caption=

主墩墩顶最大位移反应（横桥向输入）

, figureFileSmall=null, figureFileBig=null, tableContent=
地震动编号墩顶最大位移地震动编号墩顶最大位移
无控制/cmTMDI控制/cm减震率/%无控制/cmTMDI控制/cm减震率/%
167.8735.08-48.317221.96107.73-51.46
214.458.63-40.2884.5335.09674.61
333.6217.40-48.259148.7168.71-53.80
42.774.9578.701039.4626.36-33.20
59.8425.99164.13
6152.38222.3545.92均值695.59552.29-20.60
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基于TMDI的高墩大跨连续刚构桥地震反应控制
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代建成 1 , 巩亚琦 2 , 张凯林 3 , 童磊 1 , 王东升 1 , 葛笑 1 , 刘彦辉 4
地震工程与工程振动 | 2025,45(2): 118-126
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地震工程与工程振动 | 2025, 45(2): 118-126
基于TMDI的高墩大跨连续刚构桥地震反应控制
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代建成1 , 巩亚琦2, 张凯林3, 童磊1, 王东升1 , 葛笑1, 刘彦辉4
作者信息
  • 1.河北工业大学 土木与交通学院，天津 300401
  • 2.中交基础设施养护集团有限公司，北京 100011
  • 3.中冀建勘集团有限公司，河北 石家庄 050227
  • 4.广州大学 工程抗震研究中心，广东 广州 510006

    • 代建成（1995—），男，博士研究生，主要从事地震工程研究。E-mail：

通讯作者:

王东升（1974—），男，教授，博士，主要从事地震工程研究。E-mail：
Seismic response mitigation of long-span continuous rigid-frame bridges with high piers based on TMDI
Jiancheng DAI1 , Yaqi GONG2, Kailin ZHANG3, Lei TONG1, Dongsheng WANG1 , Xiao GE1, Yanhui LIU4
Affiliations
  • 1.School of Civil and Transportation Engineering, Hebei University of Technology, Tianjin 300401, China
  • 2.CCCC Infrastructure Maintenance Group, Beijing 100011, China
  • 3.China Hebei Construction & Geotechnical Investigation Group Ltd., Shijiazhuang 050227, China
  • 4.Earthquake Engineering Research & Test Center of Guangzhou University, Guangzhou 510006, China
出版时间: 2025-04-24 doi: 10.13197/j.eeed.2025.0211
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摘要
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高墩大跨连续刚构桥因主墩与上部结构固结，其减震控制设计存在一定的局限性，且主梁因地震作用会存在截面开裂及预应力束应力损失等现象。惯容系统是近年发展的结构减震控制新方式，特别是将惯容器与传统调谐质量阻尼器（tuned mass damper，TMD）结合，形成的调谐质量惯容阻尼器（tuned mass-damper-inerter，TMDI）。文中以某高墩大跨连续刚构桥为例，考虑施工过程结合Midas Civil与OpenSees软件建立非线性地震反应分析模型，以10条近断层脉冲波为输入，研究了分布式设置（多个）TMDI对其地震反应的控制效果。研究结果表明：地震动沿纵桥向输入时，TMDI可有效避免主梁顶板、底板开裂，但主梁腹板受力略有增大；沿横桥向输入时，TMDI则会明显降低主跨腹板受力；当地震动双向水平输入时，TMDI无论对主梁顶板、底板，还是主跨腹板的应力都有很好的减轻作用。在桥墩反应方面，墩顶最大位移平均减震率为52%（纵桥向）和21%（横桥向），纵桥向最大弯矩减震率是31%，在横桥向TMDI虽然会放大约10%的墩底弯矩，但它可控制桥墩的（弹塑性）残余位移反应。

高墩大跨连续刚构桥  /  减震控制  /  调谐质量惯容阻尼器（TMDI）  /  OpenSees  /  时程分析

The fixed connection between the piers and the superstructure of rigid-frame bridges with high piers exhibits limitations in seismic design. Cracking of the cross-section and prestressing tendon stress loss can be found in the main girder subjected to seismic loads. The inertialr system ( i. e. tuned mass-damper-inerter, TMDI) contains an inertial container and a traditional tuned mass damper (TMD). It is a new method for structural seismic control in recent years. This study focuses a high-pier, long-span continuous rigid-frame bridge, considering the construction process and combining Midas Civil and the OpenSees to establish a nonlinear seismic response numerical model. Using 10 near-fault pulse-like ground motion records as input, this study investigates the seismic control behavior of a distributed configuration of multiple TMDIs. The results show that when the ground motion excites the bridge along the longitudinal direction, TMDIs can effectively prevent the cracking of the top and bottom slabs of the main girder, although the internal forces of the web of the main girder increase slightly. When the ground motion excites the bridge along the transverse direction, TMDIs significantly reduce the internal forces on the web of the main span. When ground motions are input in both horizontal directions, TMDIs can effectively mitigate the stress on the top slab, bottom slab, and web of the main span. Regarding the pier response, the average seismic reduction proportions of the maximum displacement at the pier top are 52% in the longitudinal direction and 21% in the transverse direction, respectively. The seismic reduction proportions of the maximum bending moment in the longitudinal direction is 31%. Although TMDIs increase the bottom bending moment of the pier by approximately 10% in the transverse direction, they effectively control the residual displacement of the bridge pier.

rigid frame bridges with high piers  /  seismic response mitigation  /  tuned mass-damper-inerter  /  OpenSees  /  time history analysis
代建成, 巩亚琦, 张凯林, 童磊, 王东升, 葛笑, 刘彦辉. 基于TMDI的高墩大跨连续刚构桥地震反应控制. 地震工程与工程振动, 2025 , 45 (2) : 118 -126 . DOI: 10.13197/j.eeed.2025.0211
Jiancheng DAI, Yaqi GONG, Kailin ZHANG, Lei TONG, Dongsheng WANG, Xiao GE, Yanhui LIU. Seismic response mitigation of long-span continuous rigid-frame bridges with high piers based on TMDI[J]. Earthquake Engineering and Engineering Dynamics, 2025 , 45 (2) : 118 -126 . DOI: 10.13197/j.eeed.2025.0211
正文
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0　引言
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在我国的西南部山区，当跨越深谷时多采用高墩大跨连续刚构桥桥型[1]，因其墩梁固结的结构体系，当建设在强震风险区时，其减震装置仅限在边墩处设置且空间有限，因此针对高墩大跨连续刚构桥的减震控制措施研究较少且实用化遇到困难[2]。根据2008年汶川地震情况，童磊等[3]使用Midas Civil建立了庙子坪大桥有限元模型，分析了该桥主梁开裂地震破坏情况。周敉等[4]提出在刚构桥过渡墩处设置拉索钢阻尼器减震支座组合黏滞阻尼器来达到减震效果。TONG等[5]提出在过渡墩处设置摩擦摆支座是控制高墩大跨连续刚构桥主梁地震开裂损伤的有效措施。
近10 a日本东北大学IKAGO等[6]团队研发了新型的耗能增效和表观质量增效的惯容系统，如调谐黏滞质量阻尼器（tuned viscous mass damper，TVMD）。MARIAN等[7]将惯容与调谐质量阻尼器（tuned mass damper，TMD）组合提出调谐质量惯容阻尼器（tuned mass-damper-interter，TMDI），通过惯容器的质量放大机制实现了性能增强，证明了相比于传统TMD，TMDI在抑制无阻尼单自由度结构的位移上更有效。张瑞甫等[8]分析了惯容系统结合TMD的不同形式，并针对多种激励形式研究其控制效果，证明了TMDI相比传统TMD更为有效。XU等[9]利用TMDI抑制大跨度桥梁的涡激振动，通过时域和频域分析研究了该系统的控制性能和鲁棒性。DAI等[10]基于负刚度效应、质量放大效应和鲁棒性讨论了结构控制效果和优化设计参数等问题。张大光[11]将TMDI应用到悬索桥的涡激振动控制中，并使用遗传算法探究了多重调谐质量惯容阻尼器（multiple tuned mass dampers inerter，MTMDI）的优化布置。刘欣鹏等[12]通过定点理论推导了TMDI参数设计的优化公式。王玉梅等[13]对TMD、TMDI和TVMD等减振技术的设计思路和技术原理进行了对比。
目前，将TMDI用于高墩大跨连续刚构桥减震控制的研究尚少，特别是涉及主梁局部应力和桥梁结构整体反应方面。本文以某3跨百米墩高连续刚构桥为例，以近断层地震动为输入，研究了TMDI对该桥的减震效果，以期为类似桥梁减震控制提供新的思路。
1　工程概况及有限元模型
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1.1　工程概况
选取我国西南强震危险区某高墩大跨连续刚构桥为研究对象，跨径布置为125+220+125 m，引桥为跨径50 m的简支T梁桥，如图1所示。其桥墩（2#、3#、4#、5#、6#和7#墩）墩高分别为31、68、102、100、85、87 m，主墩4#墩和5#墩为矩形空心墩，采用群桩基础。主桥过渡墩处支座为盆式橡胶支座。主梁采用C60混凝土，桥墩采用C40混凝土。该桥场地基本烈度为Ⅷ度（0.2 g），Ⅱ类场地。
1.2　有限元模型
首先使用Midas Civil建立该桥考虑施工阶段的有限元模型，全桥共划分34个施工阶段。石岩等[14-15]研究表明，对悬臂浇筑的刚构桥，若不考虑施工过程主梁内力状态的影响，地震反应分析结果会存在较大的不准确性。参考其做法将Midas Civil施工阶段分析结果引入到OpenSees中，建立了考虑主梁开裂、支座及挡块损伤、桥墩非线性和TMDI阻尼器的桥梁三维非线性地震反应分析模型。因场地较硬及桩基深入岩层之中，可以忽略土-结相互作用的影响。采用瑞利阻尼模型，取横、纵桥向主振型的自振周期计算，前者对应T1 =3.16 s，后者对应T2 =2.39 s，阻尼比取5%。
基于OpenSees平台建立有限元模型，过渡墩支座采用flat-Slider-Bearing单元，引桥橡胶支座采用Elastomeric-Bearing-Plasticity单元。主、引桥的碰撞采用MUTHUKUMAR[16]提出的简化Hertz-damp碰撞单元模拟，以SILVA等[17]提出的单元来模拟横桥向挡块损伤过程。根据Midas试算结果，OpenSees建模时主墩在墩顶、墩底和边墩墩底处，主梁在根部（主墩两侧）、跨中和边跨合龙段和1/2跨中梁段处采用非线性纤维梁柱单元模拟，这些单元位置对应于关键截面。其它部位单元采用弹性梁柱单元模型，如图2所示。混凝土和钢筋分别采用Concrete02和Steel02材料本构模拟。
1.3　TMDI参数确定及模拟
TMDI是由传统的TMD系统加入惯容元件发展而来的[18-19]。目前惯容单元在OpenSeesV3.3.0中已经实现[20-21]，其单元名称为inerter。使用OpenSees内置的惯容单元inerter模拟惯容器，配合two-Node-Link单元模拟阻尼和弹簧材料，三者并联后一端与主梁共用节点，另一端为质量块节点，进而实现整个TMDI的模拟。
算例桥梁主箱梁内部共布置9个TMDI，其中T_1和T_2仅纵桥向运动，H_1为横桥向，S_1~S_6为双向都可运动，如图3所示。在主箱梁内部布置单向滑轨，横桥向（纵桥向）TMDI的质量块可在对应方向上独立运动。双向TMDI的横桥向和纵桥向的设计参数（阻尼和刚度）相互独立但质量块相同。在确定纵桥向、横桥向布置TMDI参数时，基于定点理论[12]，分别根据纵桥向和横桥向的振型确定了初步的优化参数，前者对应全桥第二振型，后者对应全桥第一振型。目前考虑多振型影响的TMDI参数优化计算方法仍在努力探索中。
最终取单个TMDI的质量块质量为20 t，由于惯容器产生的等效质量可以为自身质量的百倍，因此忽略惯容器自身质量，设置惯质比为1，其惯容器的等效质量也为20 t。纵桥向弹簧刚度为263.58 kN/m，阻尼为1.63 kN•s/m。横桥向优化设计弹簧刚度为158 kN/m，阻尼为1.26 kN•s/m。
2　地震反应与减震控制
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童磊等[3，22]给出了高墩大跨连续刚构桥的抗震薄弱环节，主要为主梁开裂、桥墩屈服和支座、挡块及伸缩缝的损伤，认为当地震动峰值达到0.3 g及以上时，主梁就会产生开裂破坏。本研究主要关注于主梁和桥墩（4#主墩）的反应。
2.1　地震动输入
选择10组近断层地震动为输入，每组包括2个水平分量和1个垂直分量。分析时考虑了3种工况：①纵桥向水平+竖向；②横桥向水平+竖向；③三向输入。输入时水平方向加速度峰值调整为0.3 g，竖向调整为水平向地震动峰值的2/3倍。输入地震动的详细信息如表1所示。
2.2　TMDI减震控制分析
高墩大跨连续刚构桥的主梁一般采用大箱梁，也就是说在横、纵桥向均有一定的空间可以安装调谐质量类阻尼器。本文分别考虑地震波沿纵桥向、横桥向和水平双向输入，以更好的考察TMDI减震控制效果。
2.2.1　TMDI纵桥向减震控制
1）主梁开裂应力控制
地震动沿桥梁纵桥向输入，设置分布式TMDI后，算例桥梁在近断层地震动（PGA为0.3 g）作用下主梁的受拉和受压应力均有一定程度的减小，基本控制了主梁顶板和底板的开裂反应，而腹板相对来说控制效果不好。图4给出了7号地震动作用下主梁开裂应力的控制效果，设置TMDI后主梁顶板、底板的拉应力明显降低，跨中合龙段位置腹板的拉应力则有些许放大。整体来看，设置分布式TMDI对主梁开裂控制效果较好。
2）主墩弯矩反应控制
表2和表3给出了分布式TMDI在纵桥向地震动输入时，对于墩顶和墩底弯矩的控制效果。就数据分析，对于墩顶弯矩平均减震率达到了42%，对于墩底弯矩的平均减震率达到31%。可见，设置TMDI后对于刚构桥墩顶的减震效果要优于对于墩底的减震效果。图5给出了6号、7号和9号地震动下墩身弯矩反应包络以及有控与无控情况下的对比。
3）主墩位移反应控制
当刚构桥出现位移时TMDI会向着相反的方向运动，从而起到限制的效果。表4给出了TMDI对于主墩墩顶位移反应的控制效果，平均减震率达到52%。作为参考，图6给出了6号、7号和9号地震动作用下的墩顶位移反应时程。
2.2.2　TMDI横桥向减震控制
1）主梁开裂应力控制
在10条近断层地震动沿横桥向输入时，分布式设置的TMDI，对于刚构桥主梁顶板和底板的减震效果不是很好。甚至TMDI会放大主梁部分关键截面底板的压应力，但对于主梁腹板拉应力的控制效果很好。同样，图7给出了7号地震动作用下主梁拉应力和压应力的变化情况。
2）主墩弯矩反应控制
表5给出了分布式布置TMDI，桥墩弯矩的控制效果，整体上TMDI会导致桥墩横桥向墩底弯矩略有放大，平均放大了约10.15%。图8给出了在6号、7号和9号地震动作用下横桥向墩身弯矩变化情况。
3）主墩位移反应控制
表6给出了设置分布式TMDI，对于墩顶位移的影响及减震效果，放大及减小的可能均存在，平均位移减震率为20.60%。图9给出了6号、7号和9号地震动作用下的刚构桥墩顶位移反应时程，这部分最大的发现是在部分地震动输入下，桥墩已经进入到了屈服阶段，设置IMDI后则显著降低了桥墩的残余位移反应。
2.2.3　TMDI双向减震控制
地震动以水平双向输入，分布式布置的TMDI将共同进行减震控制。图10给出了7号地震动（TCU054）作用下主梁拉应力和压应力的变化情况，在前述单向地震动输入时已经表明其地震反应最为不利。由图知，分布式设置TMDI双向减震控制时，对于主梁顶板、底板和主跨腹板均有很好的控制效果，对边跨腹板应力控制要弱。降低了主梁的拉、压应力响应，尤其是大大降低了底板和顶板的拉、压应力，降低了跨中腹板的拉、压应力，可以避免主梁的混凝土开裂和压溃现象的出现。
3　关于TMDI的若干讨论
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在主桥箱梁内部布置调谐质量类的阻尼器，首先需要控制其质量块的质量不能过大，否则无论是空间，还是局部应力都会导致过大。本文TMDI质量块加上惯容本身质量约为30 t，全桥9个TMDI，其中6个TMDI为横纵向共用质量块，合计约330 t，与全桥9万余吨的质量相比要小的多，甚至可以忽略。其次控制阻尼器质量块相对位移也十分重要的。研究表明，TMDI质量块与结构的纵桥向相对位移最大约为1.2 m，横桥向最大相对位移为1.4 m，而箱梁内部宽度接近12 m，完全可以满足TMDI质量块对行程的要求。
图11和图12分别给出了墩顶与TMDI质量块位移反应的比较，纵桥向可见明显的相向运动，而横桥向则表现为与结构有着些许相位差的同向运动，这可能是导致主墩横桥向受力有所增加的原因，具体仍需要进一步研究。
4　结论
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本文研究了利用分布式TMDI控制高墩大跨连续刚构桥地震反应的可行性及效果。以某高墩大跨连续刚构桥为例，基于OpenSees平台建立了全桥考虑内力状态的非线性地震反应分析模型，分别以横、纵桥向主要振型对应的周期和阻尼比，确定了各自对应的分布式TMDI及其优化模型参数。采用10条近断层地震动为输入，分析了TMDI对于主梁开裂和桥墩反应的控制效果，得出如下主要结论：
1）沿纵桥向输入地震动时，分布式设置TMDI对主梁顶板和底板开裂有较好的控制效果，但会略放大主梁腹板的应力；其可很大程度降低主墩墩顶和墩底截面的弯矩反应，墩顶位移的平均减震率约为52%。
2）沿横桥向输入地震动时，分布式设置TMDI对主梁顶板和底板拉应力的影响不明显，但对主跨的腹板拉应力控制效果很好；其会略放大横桥向墩底弯矩反应，墩顶位移平均减震率仍可达到21%，且对桥墩横桥向残余位移也有着很好的降低。
3）地震动双向输入时，分布式设置TMDI对主梁顶板、底板和主跨腹板的拉压应力均有明显的降低，可以避免开裂现象的出现。但对于边跨腹板的应力控制效果较弱。
4）分布式TMDI横、纵桥向最大位移行程分别为1.4 m和1.2 m，主梁（箱梁）内部可以为其提供足够安装及行程空间。
基金
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  • 国家自然科学基金项目(52178473)
  • 广东省地震工程与应用技术重点实验室开放基金项目(2020B1212060071)
文献
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XIE Liyu, BAN Xinlei, KANG Jianfei, et al. Study on a simple design method for direct connected cable inerter system based on modal participation cancellation[J]. Earthquake Engineering and Engineering Dynamics, 2022, 42(6): 104-113. (in Chinese)
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2025年第45卷第2期
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doi: 10.13197/j.eeed.2025.0211
  • 接收时间：2024-10-22
  • 首发时间：2026-03-20
  • 出版时间：2025-04-24
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  • 收稿日期：2024-10-22
  • 修回日期：2024-12-05
基金
国家自然科学基金项目(52178473)
广东省地震工程与应用技术重点实验室开放基金项目(2020B1212060071)
作者信息
    1.河北工业大学 土木与交通学院，天津 300401
    2.中交基础设施养护集团有限公司，北京 100011
    3.中冀建勘集团有限公司，河北 石家庄 050227
    4.广州大学 工程抗震研究中心，广东 广州 510006

通讯作者:

王东升（1974—），男，教授，博士，主要从事地震工程研究。E-mail：
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https://castjournals.cast.org.cn/joweb/dzgcygczd/CN/10.13197/j.eeed.2025.0211
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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