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Article(id=1244334014098686386, tenantId=1146029695717560320, journalId=1243988319449690156, issueId=1244334009858240758, articleNumber=null, orderNo=null, doi=10.19994/j.cnki.WEE.2025.0060, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1741104000000, receivedDateStr=2025-03-05, revisedDate=1747670400000, revisedDateStr=2025-05-20, acceptedDate=null, acceptedDateStr=null, onlineDate=1774601947568, onlineDateStr=2026-03-27, pubDate=1759248000000, pubDateStr=2025-10-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774601947568, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774601947568, creator=13701087609, updateTime=1774601947568, updator=13701087609, issue=Issue{id=1244334009858240758, tenantId=1146029695717560320, journalId=1243988319449690156, year='2025', volume='41', issue='4', pageStart='1', pageEnd='211', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1774601946558, creator=13701087609, updateTime=1774602401281, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244335917167657884, tenantId=1146029695717560320, journalId=1243988319449690156, issueId=1244334009858240758, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244335917167657885, tenantId=1146029695717560320, journalId=1243988319449690156, issueId=1244334009858240758, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=64, endPage=73, ext={EN=ArticleExt(id=1244334014358733236, articleId=1244334014098686386, tenantId=1146029695717560320, journalId=1243988319449690156, language=EN, title=A Study on vulnerability analysis method of reinforced concrete continuous girder bridge considering strong aftershocks, columnId=null, journalTitle=World Earthquake Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In the event of a continuous earthquake, strong aftershocks pose a significant threat to the bridge structures. In the analysis of seismic vulnerability, in order to consider the influence of strong aftershocks, a structural vulnerability analysis method based on spatial fitting is proposed. Taking a three-span continuous girder bridge as the object, a piecewise binary linear function is used to construct the probabilistic seismic demand model. The fitting effect and reliability of the probabilistic seismic demand model are compared and analyzed when the peak ground acceleration (PGA), peak ground velocity (PGV) and spectral acceleration (Sa) of ground motion were taken as the seismic intensity measure, and the vulnerability of the bridge in mainshock-aftershock (MS-AS) sequences based on spatial and single-sided fitting is analyzed respectively. The results show that the results of vulnerability of the bridge based on spatial fitting reflect the damage of strong aftershocks to bridges, which can effectively avoid underestimating the exceedance probability of bridges under main aftershocks. Furthermore, the probabilistic seismic demand model obtained by spatial fitting method can more accurately explain the relationship between seismic demand and structural damage. When the spectral acceleration is selected as the seismic intensity parameter, the fitting effect of the model under MS-AS sequences is the best. Additionally, the growth rate of the exceeding probability of the limit state of the bridge is dominated by the mainshock in the MS-AS sequences. The growth of the aftershock intensity has a greater impact on the exceeding probability in the vulnerability analysis based on the spatial fitting, which is conducive to the conservative estimation of the seismic performance of the bridge. The vulnerability assessment method of the bridge can provide reference for the design of highway bridge.

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在发生连续地震时，强余震对桥梁结构造成严重危害。在地震易损性分析中，为考虑强余震的影响，提出基于空间拟合的结构易损性分析方法，以一座三跨连续梁桥为对象，采用分段式的二元一次函数构建概率地震需求模型，对比分析了以地震动峰值加速度、峰值速度和谱加速度为地震强度指标时，概率地震需求模型的拟合效果和可靠性，并分别对基于空间和单面拟合的主余震桥梁结构易损性进行分析。结果表明：基于空间拟合的主余震结构易损性分析结果体现了强余震对桥梁的损害，能有效避免低估桥梁在强余震作用下的超越概率。利用空间拟合方法获取的概率地震需求模型能更准确地解释地震需求和结构损伤的关系；选取谱加速度作为地震强度参数时，主余震作用下模型的拟合效果最好。主余震作用中的强震主导了桥梁极限状态超越概率的增长速度，基于空间拟合的易损性分析中余震强度的增长对超越概率的影响更大，这有利于对桥梁抗震性能的保守估计。该桥梁易损性评估方法可为公路梁桥设计提供参考。

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曹竞（1999—），男，硕士，主要从事建筑及结构物抗震减灾。E-mail：
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李悦（1979—），男，教授，博士，主要从事建筑及结构物抗震减灾。E-mail：

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李悦（1979—），男，教授，博士，主要从事建筑及结构物抗震减灾。E-mail：

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李悦（1979—），男，教授，博士，主要从事建筑及结构物抗震减灾。E-mail：

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(in Chinese), articleTitle=Seismic vulnerability analysis of precast segmental bridge piers, refAbstract=null), Reference(id=1244335221647192141, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334014098686386, doi=null, pmid=null, pmcid=null, year=2008, volume=28, issue=4, pageStart=13, pageEnd=19, url=null, language=null, rfNumber=[24], rfOrder=36, authorNames=刘良林, 王全凤, 沈章春, journalName=地震, refType=null, unstructuredReference=刘良林, 王全凤, 沈章春. 基于损伤的累积滞回耗能与延性系数[J]. 地震, 2008, 28(4): 13-19., articleTitle=基于损伤的累积滞回耗能与延性系数, refAbstract=null), Reference(id=1244335221756244050, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334014098686386, doi=null, pmid=null, pmcid=null, year=2008, volume=28, issue=4, pageStart=13, pageEnd=19, url=null, language=null, rfNumber=[24], rfOrder=37, authorNames=LIU Lianglin, WANG Quanfeng, SHEN Zhangchun, journalName=Earthquake, refType=null, unstructuredReference=LIU Lianglin, WANG Quanfeng, SHEN Zhangchun. 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Information of selected earthquake events

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序号地震事件主震震级余震震级
1Chi-Chi7.626.30
2Chalfant Valley6.405.80
3Umbria Marche6.005.50
4Friuli6.505.91
5Imperial Valley6.535.01
6Irpinia6.906.20
7Livermore5.805.42
8Mammoth Lakes6.065.69
9Northridge6.696.05
10Whittier Narrows5.995.27
), ArticleFig(id=1244335215859053444, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334014098686386, language=CN, label=表1, caption=

所选地震事件信息

, figureFileSmall=null, figureFileBig=null, tableContent=
序号地震事件主震震级余震震级
1Chi-Chi7.626.30
2Chalfant Valley6.405.80
3Umbria Marche6.005.50
4Friuli6.505.91
5Imperial Valley6.535.01
6Irpinia6.906.20
7Livermore5.805.42
8Mammoth Lakes6.065.69
9Northridge6.696.05
10Whittier Narrows5.995.27
), ArticleFig(id=1244335215951328137, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334014098686386, language=EN, label=Table 2, caption=

Drift rate Dr and standard deviation βc under different damage states

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损伤状态轻微损伤(LS1)中等破坏(LS2)严重破坏(LS3)完全倒塌(LS4)
βc0.590.510.640.65
Dr/%[0.33,0.52)[0.52,1.08)[1.08,2.39)[2.39,+∞)
), ArticleFig(id=1244335216039408527, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334014098686386, language=CN, label=表2, caption=

不同损伤状态下的漂移率Dr和标准差βc

, figureFileSmall=null, figureFileBig=null, tableContent=
损伤状态轻微损伤(LS1)中等破坏(LS2)严重破坏(LS3)完全倒塌(LS4)
βc0.590.510.640.65
Dr/%[0.33,0.52)[0.52,1.08)[1.08,2.39)[2.39,+∞)
), ArticleFig(id=1244335216131683219, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334014098686386, language=EN, label=Table 3, caption=

Parameter fitting results

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拟合方式IM a b c R2 R2（IMA<IMM） R2（IMA≥IMM）
空间PGA-4.0210.6910.1070.4150.5130.316
 PGV-3.3981.0090.0410.7530.8160.689
 Sa-5.7901.0300.0450.7850.8050.764
单面PGA-3.9210.5540.2280.4050.4560.054
 PGV-3.5930.8270.2270.7460.7970.307
 Sa-5.4840.8150.2310.7530.7320.132
), ArticleFig(id=1244335216244929433, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334014098686386, language=CN, label=表3, caption=

参数拟合结果

, figureFileSmall=null, figureFileBig=null, tableContent=
拟合方式IM a b c R2 R2（IMA<IMM） R2（IMA≥IMM）
空间PGA-4.0210.6910.1070.4150.5130.316
 PGV-3.3981.0090.0410.7530.8160.689
 Sa-5.7901.0300.0450.7850.8050.764
单面PGA-3.9210.5540.2280.4050.4560.054
 PGV-3.5930.8270.2270.7460.7970.307
 Sa-5.4840.8150.2310.7530.7320.132
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考虑强余震的钢筋混凝土桥梁易损性分析方法研究
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李悦 1 , 曹竞 2 , 张常勇 3 , 李冲 4 , 黄帅 5
世界地震工程 | 第十三届全国防震减灾工程学术研讨会优秀论文专栏 2025,41(4): 64-73
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世界地震工程 | 第十三届全国防震减灾工程学术研讨会优秀论文专栏 2025, 41(4): 64-73
考虑强余震的钢筋混凝土桥梁易损性分析方法研究
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李悦1 , 曹竞2 , 张常勇3, 李冲4, 黄帅5
作者信息
  • 1.北方工业大学土木工程学院，北京　100144
  • 2.南昌大学建筑与设计学院，江西　南昌　330031
  • 3.山东省交通规划设计院集团有限公司，山东　济南　250031
  • 4.中交公路长大桥建设国家工程研究中心有限公司，北京　100088
  • 5.应急管理部国家自然灾害防治研究院，北京　100085

    • 李悦（1979—），男，教授，博士，主要从事建筑及结构物抗震减灾。E-mail：

通讯作者:

曹竞（1999—），男，硕士，主要从事建筑及结构物抗震减灾。E-mail：
A Study on vulnerability analysis method of reinforced concrete continuous girder bridge considering strong aftershocks
Yue LI1 , Jing CAO2 , Changyong ZHANG3, Chong LI4, Shuai HUANG5
Affiliations
  • 1.School of Civil Engineering, North China University of Technology, Beijing 100144, China
  • 2.Architecture & Design College, Nanchang University, Nanchang 330031, China
  • 3.Shandong Traffice Planning and Design Institute, Jinan 250031, China
  • 4.CCCC Highway Bridges National Engineering Research Centre Co., Ltd., Beijing 100088, China
  • 5.National Institute of Natural Hazards, Ministry of Emergency Management of P.R. China, Beijing 100085, China
出版时间: 2025-10-01 doi: 10.19994/j.cnki.WEE.2025.0060
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摘要
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在发生连续地震时，强余震对桥梁结构造成严重危害。在地震易损性分析中，为考虑强余震的影响，提出基于空间拟合的结构易损性分析方法，以一座三跨连续梁桥为对象，采用分段式的二元一次函数构建概率地震需求模型，对比分析了以地震动峰值加速度、峰值速度和谱加速度为地震强度指标时，概率地震需求模型的拟合效果和可靠性，并分别对基于空间和单面拟合的主余震桥梁结构易损性进行分析。结果表明：基于空间拟合的主余震结构易损性分析结果体现了强余震对桥梁的损害，能有效避免低估桥梁在强余震作用下的超越概率。利用空间拟合方法获取的概率地震需求模型能更准确地解释地震需求和结构损伤的关系；选取谱加速度作为地震强度参数时，主余震作用下模型的拟合效果最好。主余震作用中的强震主导了桥梁极限状态超越概率的增长速度，基于空间拟合的易损性分析中余震强度的增长对超越概率的影响更大，这有利于对桥梁抗震性能的保守估计。该桥梁易损性评估方法可为公路梁桥设计提供参考。

主余震  /  连续梁桥  /  地震动强度参数  /  易损性曲面  /  空间拟合

In the event of a continuous earthquake, strong aftershocks pose a significant threat to the bridge structures. In the analysis of seismic vulnerability, in order to consider the influence of strong aftershocks, a structural vulnerability analysis method based on spatial fitting is proposed. Taking a three-span continuous girder bridge as the object, a piecewise binary linear function is used to construct the probabilistic seismic demand model. The fitting effect and reliability of the probabilistic seismic demand model are compared and analyzed when the peak ground acceleration (PGA), peak ground velocity (PGV) and spectral acceleration (Sa) of ground motion were taken as the seismic intensity measure, and the vulnerability of the bridge in mainshock-aftershock (MS-AS) sequences based on spatial and single-sided fitting is analyzed respectively. The results show that the results of vulnerability of the bridge based on spatial fitting reflect the damage of strong aftershocks to bridges, which can effectively avoid underestimating the exceedance probability of bridges under main aftershocks. Furthermore, the probabilistic seismic demand model obtained by spatial fitting method can more accurately explain the relationship between seismic demand and structural damage. When the spectral acceleration is selected as the seismic intensity parameter, the fitting effect of the model under MS-AS sequences is the best. Additionally, the growth rate of the exceeding probability of the limit state of the bridge is dominated by the mainshock in the MS-AS sequences. The growth of the aftershock intensity has a greater impact on the exceeding probability in the vulnerability analysis based on the spatial fitting, which is conducive to the conservative estimation of the seismic performance of the bridge. The vulnerability assessment method of the bridge can provide reference for the design of highway bridge.

main shock-aftershock  /  continuous girder bridge  /  ground motion intensity measure  /  vulnerability surface  /  spatial fitting
李悦, 曹竞, 张常勇, 李冲, 黄帅. 考虑强余震的钢筋混凝土桥梁易损性分析方法研究. 世界地震工程, 2025 , 41 (4) : 64 -73 . DOI: 10.19994/j.cnki.WEE.2025.0060
Yue LI, Jing CAO, Changyong ZHANG, Chong LI, Shuai HUANG. A Study on vulnerability analysis method of reinforced concrete continuous girder bridge considering strong aftershocks[J]. World Earthquake Engineering, 2025 , 41 (4) : 64 -73 . DOI: 10.19994/j.cnki.WEE.2025.0060
正文
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0　引言
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在地震灾害中，结构在遭受主震冲击后，往往还面临多次余震的二次冲击[1]，其中高强度余震对结构的危害不容忽视，如2004年日本新潟中越地震、2008年汶川地震和2011年东日本大地震中都发生了高强度余震，致使大量结构完全倒塌[2-3]。而地震易损性分析反映了地震动强度与结构损坏程度之间的关系[4]，能为结构在主余震作用下进行风险评估提供重要依据[5]。但现有方法往往采用地震峰值加速度或峰值位移等地震强度指标（intensity measure，IM）来衡量地震强度[6]。而单一的地震动强度参数不能全面反映地震动特性，导致易损性评估与实际存在较大偏差[7]。因此开展考虑强余震的结构易损性研究十分必要。
为提高结构地震易损性分析的可靠性，常采用多个地震强度指标进行易损性分析，苏琪等[7]对高速公路隧道开展了同时考虑地震震级和地震动峰值加速度的易损性分析，通过对比美国生命线联盟ALA（American Lifelines Alliance）中的经验易损性曲线验证了所提分析方法的合理性；张建辉等[8]选取地震动峰值加速度和加速度反应谱强度构建矢量地震强度指标对结构进行易损性分析，发现考虑矢量地震强度指标能有效提高对结构损伤预测的准确性；林峻岑等[9]分别基于单一地震强度指标IM和双地震强度指标IMs对隧道结构展开易损性分析，结果表明采用双地震强度指标能有效降低结构损伤预测的离散性。而为了更准确地评估主余震作用下结构的易损性，ZHOU等[10]对建筑结构进行了基于双地震强度参数的主余震结构易损性分析，发现结构的损伤概率受余震强度影响较大，仅考虑主震的易损性分析严重低估了主余震序列作用下的超越概率；CHEN等[11]建立同时考虑主震和余震强度的矢量地震强度指标，用以分析主余震作用下高墩梁桥的地震易损性，结果表明忽略高强度余震会低估结构的超越概率。
为在易损性分析中更充分考虑强余震对结构损伤的影响，文中提出基于空间拟合的主余震作用下桥梁易损性评估方法，采用分段式二元一次函数独立考虑到强余震对结构损伤的影响，以地震动峰值加速度（peak ground acceleration，PGA）、地震动峰值速度（peak ground velocity，PGV）和谱加速度（spectral asseleration，Sa）体现地震强度，并对所构建的概率地震需求模型的可靠度进行对比，获得更准确有效的地震强度指标，分别对比基于空间拟合和单面拟合的桥梁极限状态超越概率，得到能更准确反映主余震特性的易损性分析方法。提出的基于空间拟合的主余震桥梁易损性评估框架如图1所示。
1　桥梁有限元模型建立
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以我国典型三跨三柱式钢筋混凝土连续梁桥（3×25 m）为对象，桥梁采用钢筋混凝土T型梁，桥墩高4.6 m，直径0.9 m。桥墩混凝土为C40，钢筋为HRB400。墩梁间采用板式橡胶支座。基于OpenSees平台建立桥梁动力分析模型。主梁、盖梁和桥台采用弹性梁单元模拟。桥墩在地震作用下表现出非线性特性，因此采用基于位移的纤维梁单元模拟，支座采用弹塑性支座单元支座本构模型进行模拟，该单元良好的线弹性特征可以较为准确地模拟橡胶几何及材料非线性。选用双曲型间隙材料模型以模拟桥台后的填土作用。采用碰撞本构模型材料模拟桥台与主梁碰撞时的力与位移变化。混凝土材料本构采用混凝土木构模型，通过改变混凝土受压骨架曲线的峰值应力、峰值应变以及软化段斜率来考虑箍筋的约束影响。钢筋采用能够考虑等向应变硬化影响的钢筋本构模型。桥梁模型示意和上述材料本构信息如图2所示。
2　主余震地震记录选取与合成
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由于地震动具有极强的随机性，为了真实地反映地震特性，从美国太平洋地震工程研究中心（Pacific Earthquake Engineering Research Center，PEER）强震记录数据库[12]中选取了120条真实主余震记录，表1展示了所选的地震事件。将主余震地震记录构造为主余震序列时，选择相同台站和方向的同一次地震[13]，当连续发生多次余震时，选取强度最大的构造主余震序列[14]，余震震级不小于M5.0[15-16]。选取的地震动震级、断层距分布和反应谱如图3所示。为确保结构在主震后能够重新到达平衡位置，以模拟主余震之间的地震激励间隔，在主余震间设置30 s的间隔，保证余震发生前，结构处于静止状态[11，17-18]。主余震合成示意如图4所示。
所选取地震记录的PGA、PGV和Sa的分布如图5所示。尽管所选取地震的主震震级皆大于余震，但仍有部分余震的强度高于主震。如在16.7%的地震中，余震的PGA高于主震，而在18.3%和10.8%的地震中，PGV和Sa分别高于主震。该研究将这类地震强度指标（即PGA、PGV或Sa）高于主震的余震定义为强余震[18]。因此，在桥梁易损性分析时考虑高强度余震的影响是十分必要的。
3　考虑主余震的桥梁易损性分析
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3.1　易损性分析方法
为考虑主、余震地震强度和强余震计算结果对易损性评估的不利影响，提出基于空间拟合的易损性分析方法，结构在主余震作用下的超越概率可表示为
式中：D为地震需求参数；C为抗震能力参数；Φ[•]为标准正态累积分布函数[19]；IMM和IMA分别表示为主震和余震的地震强度；SD-MA和SC分别为结构主余震地震需求和抗震能力的对数均值；βC为结构抗震能力的对数标准差，仅与结构自身能力相关，取值见表2[20]。βMA为结构在主余震作用下地震需求的对数标准差，可通过式（2）计算：
式中：为主余震作用下桥梁的地震需求；SD-MA是地震需求参数的平均值；N为地震数量。当同时考虑主、余震强度时，服从对数正态分布的地震需求参数SD-MA与地震动强度参数IM的对数线性关系[21]，可通过二元一次函数进行单面拟合，如式（3）[22]：
式中：a、b和c是基于地震需求和地震强度结果拟合的回归系数。为更恰当考虑强余震作用下的结构损伤，根据主、余震地震强度参数的分布，以IMA=IMM为界限对结构损伤进行分组。当IMA<IMM时，以二元一次函数拟合SD-MA与IM的关系。当IMA>IMM时，以沿IMA=IMM对称的函数概括SD-MA与IM的关系，如式（4）所示。
在进行桥梁易损性分析时，为了反映桥梁的地震需求SD-MA和抗震能力SC，选取桥墩漂移率Dr作为评价桥梁易损性的工程需求参数[23]，其计算方法见式（5）：
式中：H为墩高；Dc为墩顶最大水平向位移。为获取桥梁各损伤状态下对应的桥墩漂移率Dr，采用等效能量法[24]提取桥墩力-位移曲线中的开裂点、屈服点、峰值点和极限点对应的位移，如图6所示。其中，Dcr为保护层混凝土首次开裂时的墩顶位移，Dy为桥墩屈服时的墩顶位移，Dm为桥墩达到最大承载力时的墩顶位移，Du为桥墩达到极限变形时的墩顶位移。依据特征点对应的位移并通过式（5）计算获取了各损伤状态下桥墩漂移率的范围，见表2。
3.2　基于空间拟合的桥梁地震易损性分析
对连续梁桥有限元模型进行非线性时程分析，获得P1-C2桥墩漂移率Dr，由式（3）和式（4）分别获取了主余震作用下基于单面拟合和空间拟合的桥梁概率地震需求模型（probabilistic seismic demand model，PSDMs）。图7分别展示了采用PGA、PGV和Sa对Dr的对数拟合结果，表3给出了拟合的各参数数值，其中R2为概率地震需求模型的决定系数，用以衡量模型的预测能力，反映了拟合效果的优劣。
由表3可知，当采用Sa作为地震强度指标时，构建概率地震需求模型的拟合效果显著优于PGA和PGV。在对SD-MA和IM进行单面拟合时，以Sa为地震强度指标的概率地震需求模型决定系数R2为0.753，分别高于以PGA和PGV为地震强度指标时的0.445和0.746；在进行空间拟合时，以Sa为地震强度指标在IMA<IMM和IMA≥IMM空间内的R2可达0.805和0.764，平均为0.785，分别高于PGA和PGV的0.315和0.753。
构建概率地震需求模型时，由于基于空间拟合的概率需求模型的决定系数R2比单面拟合更高，如采用Sa为地震强度指标时，基于空间拟合的模型决定系数R2为0.785，大于单面拟合的0.753。而当发生强余震时（IMA≥IMM），基于空间拟合的模型决定系数R2为0.764，显著高于单面拟合的0.132。由此可见，空间拟合方法的拟合精度整体高于单面拟合，特别是在发生强余震时，极大提高了拟合的精度。发生强余震作用时，桥梁损伤程度与发生强主震时相当，双阶段拟合更契合主余震作用下的桥梁损伤分布，因此采用空间拟合相比单面拟合能更准确地反映地震强度与结构损伤的关系。
由图7（c）可知，采用单面拟合的概率需求模型的预测结果与强余震计算结果有较大误差，未能考虑强余震导致的结构损伤。采用空间拟合方法将强余震计算结果单独考虑，构建概率需求模型时能恰当考虑强余震情景，大幅减少强余震下模型预测结果与计算结果的误差，也避免了强余震下的损伤计算结果对强主震时（IMA<IMM）的预测结果的干扰。
基于已建立的地震需求模型和预定义的损伤状态，对比分析了基于空间拟合和单面拟合的桥梁易损性，如图8所示。在发生强余震时，空间拟合方法考虑了强余震导致的结构损伤，避免了易损性分析结果严重低估强余震情况下的超越概率。在发生强主震时，基于空间拟合的超越概率也高于单面拟合，提高了易损性分析时的安全冗余。采用单面拟合时，未将强余震的损伤计算结果分离处理，干扰了概率地震需求模型的预测能力，导致易损性分析结果时低估弱余震时的超越概率。发生强余震时，应采用基于空间拟合的易损性分析方法，以避免对高强度余震下的结构易损性产生低估。建议在桥梁抗震设计规范中，采用基于空间拟合的易损性分析方法，评估强余震（IMA>IMM）作用下桥梁的易损性。此外，基于空间拟合的易损性分析方法能更准确地评估桥梁在地震中的损伤情况，为震后经济损失和桥梁的抗震韧性评估提供更可靠的依据。
根据易损性曲面获取了各损伤状态超越概率的等高线投影，如图9所示。图中的线表示特定超越概率对应的主余震强度需求。可以发现，主震和余震强度变化对桥梁各损伤状态超越概率存在交互影响，主余震强度共同影响着桥梁各损伤状态超越概率。
分别从基于空间拟合的易损性曲面，截取了余震谱加速度SaA为0、2、3、4 m/s2时桥梁在各损伤状态下的超越概率，如图10所示。基于空间拟合的易损性分析能更好地反映强余震对桥梁损害，避免低估强余震下桥梁极限状态超越概率。当SaA和SaM为3 m/s2时，基于空间拟合的桥梁严重损伤超越概率与单面拟合相差0.018，而当余震强度超过主震时，如SaA为3 m/s2且SaM为3 m/s2时，基于空间拟合的桥梁严重损伤超越概率比单面拟合高0.385。
相比单面拟合，基于空间拟合的易损性分析结果中余震强度的增长对超越概率的影响更大，这有利于对桥梁抗震性能的保守估计。如SaM为3 m/s2，SaA从0 m/s2增长到4 m/s2时，基于空间拟合的严重损伤超越概率从0.029增长到0.518，增长了0.489，高于单面拟合的0.132。
桥梁极限损伤状态的超越概率随着地震强度的增长速度由主余震作用中的强震主导，当SaA>SaM时，桥梁基于双面拟合的超越概率增长缓慢，这时桥梁的各损伤状态超越概率增长受余震强度影响较大，SaM的增加仅能影响超越概率使之缓慢增长；而当SaM增长到超过SaA时，桥梁的各损伤状态超越概率增长受主震强度影响大于余震，随着SaM的增长，超越概率急剧增大。
由图10可知，同一余震强度下，随着主震强度的增长，基于空间拟合的易损性曲线呈现不同阶段，这是采用了分段函数构建地震概率需求模型导致的结果。易损性曲线呈现出不同阶段说明，强余震与强主震二者作用下的桥梁超越概率发展具有显著差异，这区别于传统易损性曲线的平滑发展，体现了强余震下桥梁的损坏风险。发生强余震时，采用基于空间拟合的易损性分析方法能更准确评估桥梁易损性。
4　结论
收起
研究了主余震作用下连续梁桥的易损性，为契合主余震地震下桥梁的损伤特点，同时考虑主震和余震的地震强度指标，开发空间拟合方法构建了地震需求模型，提出了能避免低估高强度余震下超越概率的易损性评估方法，并运用该方法获取了易损性曲面，得到以下结论：
1）提出了能考虑强余震作用下的主余震易损性分析方法，该方法采用空间拟合构建需求模型，计算简便的同时保持了较高的准确性，更能契合地震需求随主震和余震强度而变化的趋势，有效避免了低估桥梁在强余震作用下的易损性。
2）选取了PGA、PGV和Sa作为地震强度指标进行对比分析，发现选取Sa时对于主余震作用下地震强度和结构损伤关系的拟合效果最好。此外，构建概率地震需求模型时，采用空间拟合相比单面拟合能更有效地表达地震强度与结构损伤的关系。
3）在基于空间拟合的易损性分析结果中余震强度的增长对超越概率的影响更大，有利于对桥梁抗震性能的保守估计。同时，主余震作用中的强震主导了桥梁极限状态超越概率的增长速度。
基金
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  • 国家自然科学基金资助项目(51408009)
文献
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2025年第41卷第4期
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doi: 10.19994/j.cnki.WEE.2025.0060
  • 接收时间：2025-03-05
  • 首发时间：2026-03-27
  • 出版时间：2025-10-01
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  • 收稿日期：2025-03-05
  • 修回日期：2025-05-20
基金
国家自然科学基金资助项目(51408009)
作者信息
    1.北方工业大学土木工程学院，北京　100144
    2.南昌大学建筑与设计学院，江西　南昌　330031
    3.山东省交通规划设计院集团有限公司，山东　济南　250031
    4.中交公路长大桥建设国家工程研究中心有限公司，北京　100088
    5.应急管理部国家自然灾害防治研究院，北京　100085

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曹竞（1999—），男，硕士，主要从事建筑及结构物抗震减灾。E-mail：
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