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Article(id=1241791683352920312, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241791680479822062, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2025.0209, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1710259200000, receivedDateStr=2024-03-13, revisedDate=1715443200000, revisedDateStr=2024-05-12, acceptedDate=null, acceptedDateStr=null, onlineDate=1773995808684, onlineDateStr=2026-03-20, pubDate=1745424000000, pubDateStr=2025-04-24, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773995808684, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773995808684, creator=13701087609, updateTime=1773995808684, 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=97, endPage=105, ext={EN=ArticleExt(id=1241791683591995646, articleId=1241791683352920312, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Analysis of the seismic vulnerability of eccentrically supported pier columns of curved bridges under different variable pier height forms, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Due to the influence of topography and traffic routes, small radius curved bridges with eccentrically support piers and variable pier heights are widely used. Due to the irregularity of the bridge caused by the difference in pier heights and the eccentric supports, a complex stress form of pressure-bending-shearing-torsion coupling in the eccentrically support pier will occur. Taking an interchange ramp bridge as the engineering background, a centralized hinge-fiber model based on nonlinear finite element software was constructed. The seismic vulnerability of eccentrically compressed piers in two models was compared by adopting the incremental dynamic analysis method. These two models include a model with the concave-type variable height piers (the CTVHP curved bridge) and a model with gradient variable height piers (the GVHP curved bridge). The results show that: in the small radius bridge with eccentrically support pier and variable pier heights, the probability of torsional damage of the intermediate pier is higher. When the pier torsional damage occurs, the exceeding probability of each pier damage level in the CTVHP curved bridge is greater than that in the GVHP curved bridge, which will lead to more serious torsional damage. Therefore the arrangement of the CTVHP curved bridge should be avoided in seismic design, at the same time, the seismic capacity of the intermediate pier should be enhanced. The research results of this paper can provide a basis for similar bridges.

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受地形及交通线路的影响，墩柱偏心支承小半径变墩高曲线桥被广泛采用。由于不同墩高之间的差异带来的桥梁非规则性，往往导致墩柱偏心支承小半径曲线桥桥墩呈现压弯剪扭多种耦合受力。文中以某互通式立交匝道桥为工程背景，基于非线性有限元软件建立集中铰-纤维模型，采用增量动力分析法分析渐变型和凹岛型2种变墩高布置形式下墩柱偏心支承曲线桥的桥墩地震易损性。研究结果表明：在小半径偏心变墩高曲线桥中，中间墩发生扭转损伤的概率较高；当墩柱发生扭转损伤时，凹岛型下桥墩各破坏等级的超越概率大于渐变型，从而将产生更严重的扭转破坏，在抗震设计中应避免选择该布置形式或提升中间墩的抗震能力。文中相关研究成果可为同类桥梁提供依据。

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方蓉（1991—），女，博士，主要从事桥梁抗震研究。E-mail：
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焦驰宇（1980—），男，教授，博士，主要从事桥梁抗震和桥梁维修加固研究。E-mail：

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焦驰宇（1980—），男，教授，博士，主要从事桥梁抗震和桥梁维修加固研究。E-mail：

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焦驰宇（1980—），男，教授，博士，主要从事桥梁抗震和桥梁维修加固研究。E-mail：

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tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791683352920312, language=CN, orderNo=3, keyword=变墩高布置形式), Keyword(id=1241802901669090033, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791683352920312, language=CN, orderNo=4, keyword=压弯剪扭耦合作用), Keyword(id=1241802901836862207, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791683352920312, language=CN, orderNo=5, keyword=地震易损性分析)], refs=[Reference(id=1241802910070280495, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791683352920312, doi=null, pmid=null, pmcid=null, year=2012, volume=10, issue=5, pageStart=1455, pageEnd=1479, url=null, language=null, rfNumber=[1], rfOrder=0, authorNames=TONDINI N, STOJADINOVIC B, journalName=Bulletin of Earthquake Engineering, refType=null, unstructuredReference=TONDINI N, STOJADINOVIC B. 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articleId=1241791683352920312, language=EN, label=Fig. 12, caption=Comparison of vulnerability curves of the M pier under different layout forms, figureFileSmall=54Z0Do0UBx3wkLdBpgPXCw==, figureFileBig=tbjYJGWwRQ3YK+KZH4gpCA==, tableContent=null), ArticleFig(id=1241802908174454874, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791683352920312, language=CN, label=图12, caption=不同布置形式下M墩易损性曲线对比, figureFileSmall=54Z0Do0UBx3wkLdBpgPXCw==, figureFileBig=tbjYJGWwRQ3YK+KZH4gpCA==, tableContent=null), ArticleFig(id=1241802908270923877, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791683352920312, language=EN, label=Table 1, caption=

Height setting of bridge piers under different arrangement forms

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布置型式跨径布置0号1号2号3号4号
渐变型4×209151299
凹岛型4×209159129
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不同布置形式下桥墩高度设置

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布置型式跨径布置0号1号2号3号4号
渐变型4×209151299
凹岛型4×209159129
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Description of the damage state of torsionally failed bridge piers

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损伤指标损伤状态描述
无损伤桥墩表面仅产生轻微斜裂缝
轻微损伤墩身出现多条斜裂缝，并有斜裂缝形成主裂缝
中等损伤主裂缝逐渐变宽，墩身出现多处交叉贯通裂缝
完全损伤大块混凝土剥落，桥墩抗扭承载力降至8%
), ArticleFig(id=1241802908660994200, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791683352920312, language=CN, label=表2, caption=

扭转破坏型桥墩损伤状态描述

, figureFileSmall=null, figureFileBig=null, tableContent=
损伤指标损伤状态描述
无损伤桥墩表面仅产生轻微斜裂缝
轻微损伤墩身出现多条斜裂缝，并有斜裂缝形成主裂缝
中等损伤主裂缝逐渐变宽，墩身出现多处交叉贯通裂缝
完全损伤大块混凝土剥落，桥墩抗扭承载力降至8%
), ArticleFig(id=1241802908816183460, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791683352920312, language=EN, label=Table 3, caption=

Classification of the torsional failure damage level of the M pier

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布置形式无损伤轻微损伤中等损伤完全损伤
渐变型μθd≤11<μθd≤3.613.61<μθd≤5.18μθd>5.18
凹岛型μθd≤11<μθd≤3.543.54<μθd≤5.09μθd>5.09
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M墩扭转破坏损伤等级划分

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布置形式无损伤轻微损伤中等损伤完全损伤
渐变型μθd≤11<μθd≤3.613.61<μθd≤5.18μθd>5.18
凹岛型μθd≤11<μθd≤3.543.54<μθd≤5.09μθd>5.09
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不同变墩高形式下曲线桥偏心支承墩柱地震易损性分析
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焦驰宇 1, 2, 3 , 王琛琛 3 , 刘洋 4 , 方蓉 5 , 肖春 6
地震工程与工程振动 | 2025,45(2): 97-105
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地震工程与工程振动 | 2025, 45(2): 97-105
不同变墩高形式下曲线桥偏心支承墩柱地震易损性分析
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焦驰宇1, 2, 3 , 王琛琛3, 刘洋4, 方蓉5 , 肖春6
作者信息
  • 1.北京市城市交通基础设施建设工程技术研究中心，北京 100044
  • 2.北京建筑大学 工程结构与新材料北京市高等学校工程研究中心，北京 100044
  • 3.北京建筑大学古桥研究院，北京 100044
  • 4.北京工业大学 城市与工程安全减灾教育部重点实验室，北京 100124
  • 5.北京建筑大学大型多功能振动台阵实验室，北京 100044
  • 6.中恒工程设计院有限公司，四川 成都 610017

    • 焦驰宇（1980—），男，教授，博士，主要从事桥梁抗震和桥梁维修加固研究。E-mail：

通讯作者:

方蓉（1991—），女，博士，主要从事桥梁抗震研究。E-mail：
Analysis of the seismic vulnerability of eccentrically supported pier columns of curved bridges under different variable pier height forms
Chiyu JIAO1, 2, 3 , Chenchen WANG3, Yang LIU4, Rong FANG5 , Chun XIAO6
Affiliations
  • 1.Beijing Urban Transportation Infrastructure Construction Engineering Technology Research Center, Beijing 100044, China
  • 2.Beijing Higher Institution Engineering Research Center of Civil Engineering Structure and Renewable Material, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
  • 3.Ancient Bridge Research Institute, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
  • 4.Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China
  • 5.Multi-Functional Shaking Tables Laboratory, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
  • 6.Eternal Estate Engineering Design Co., Ltd., Chengdu 610017, China
出版时间: 2025-04-24 doi: 10.13197/j.eeed.2025.0209
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摘要
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受地形及交通线路的影响，墩柱偏心支承小半径变墩高曲线桥被广泛采用。由于不同墩高之间的差异带来的桥梁非规则性，往往导致墩柱偏心支承小半径曲线桥桥墩呈现压弯剪扭多种耦合受力。文中以某互通式立交匝道桥为工程背景，基于非线性有限元软件建立集中铰-纤维模型，采用增量动力分析法分析渐变型和凹岛型2种变墩高布置形式下墩柱偏心支承曲线桥的桥墩地震易损性。研究结果表明：在小半径偏心变墩高曲线桥中，中间墩发生扭转损伤的概率较高；当墩柱发生扭转损伤时，凹岛型下桥墩各破坏等级的超越概率大于渐变型，从而将产生更严重的扭转破坏，在抗震设计中应避免选择该布置形式或提升中间墩的抗震能力。文中相关研究成果可为同类桥梁提供依据。

曲线桥  /  墩柱偏心支承  /  变墩高布置形式  /  压弯剪扭耦合作用  /  地震易损性分析

Due to the influence of topography and traffic routes, small radius curved bridges with eccentrically support piers and variable pier heights are widely used. Due to the irregularity of the bridge caused by the difference in pier heights and the eccentric supports, a complex stress form of pressure-bending-shearing-torsion coupling in the eccentrically support pier will occur. Taking an interchange ramp bridge as the engineering background, a centralized hinge-fiber model based on nonlinear finite element software was constructed. The seismic vulnerability of eccentrically compressed piers in two models was compared by adopting the incremental dynamic analysis method. These two models include a model with the concave-type variable height piers (the CTVHP curved bridge) and a model with gradient variable height piers (the GVHP curved bridge). The results show that: in the small radius bridge with eccentrically support pier and variable pier heights, the probability of torsional damage of the intermediate pier is higher. When the pier torsional damage occurs, the exceeding probability of each pier damage level in the CTVHP curved bridge is greater than that in the GVHP curved bridge, which will lead to more serious torsional damage. Therefore the arrangement of the CTVHP curved bridge should be avoided in seismic design, at the same time, the seismic capacity of the intermediate pier should be enhanced. The research results of this paper can provide a basis for similar bridges.

curved bridge  /  eccentric surport pier columns  /  arrangement form of variable pier height  /  coupling action of compression-bending-shear-torsion  /  seismic vulnerability analysis
焦驰宇, 王琛琛, 刘洋, 方蓉, 肖春. 不同变墩高形式下曲线桥偏心支承墩柱地震易损性分析. 地震工程与工程振动, 2025 , 45 (2) : 97 -105 . DOI: 10.13197/j.eeed.2025.0209
Chiyu JIAO, Chenchen WANG, Yang LIU, Rong FANG, Chun XIAO. Analysis of the seismic vulnerability of eccentrically supported pier columns of curved bridges under different variable pier height forms[J]. Earthquake Engineering and Engineering Dynamics, 2025 , 45 (2) : 97 -105 . DOI: 10.13197/j.eeed.2025.0209
正文
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0　引言
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变墩高小半径曲线桥因其通行能力强和适应地形效果好等特点被广泛应用于城市、山区或丘陵道路。受交通线路的影响，墩柱偏心支承的小半径变墩高曲线桥是经常出现的一种非规则桥梁体系。但在地震作用下，由于桥梁的非规则性带来不同墩高之间的差异，导致偏心支承小半径曲线桥的桥墩呈现压-弯-剪-扭多种耦合受力[1-2]。
长期以来，国内外学者针对地震下不同墩柱高度和不同受荷形式下桥墩的破坏形态进行了大量研究，为变墩高曲线桥梁损伤状态积累了大量研究基础。BELARBI等[3]对圆形钢筋混凝土（reinforced concrete，RC）桥墩进行了往复荷载试验，加载形式主要包括：压弯曲、压扭转和压弯扭等。结果发现压弯扭耦合作用对于桥墩抗扭及抗弯承载力都起到了降低作用。KAWASHIMA等[4]以压弯扭耦合作用下方形钢筋混凝土桥墩的拟静力试验数据为基础，探究了扭转作用对于桥墩损伤状态的影响。但是针对独立墩柱的抗震试验研究，并不能获得对变墩高曲线桥梁整体抗震机理规律的深入分析。
在现有研究中，基于易损性的桥梁抗震性能评估是确定构件及体系非线性地震行为特征的重要方法。因此，为确定地震过程中的损伤破坏规律，国内外学者开展了大量的地震易损性分析。吴慎其等[5]对多维地震动作用下曲线连续桥梁地震易损性进行研究，在地震作用下曲率半径小的曲线连续梁桥更容易受损。陈静[6]通过对高墩大跨连续刚构桥进行地震易损性分析，结果表明墩柱易发生损伤，尤其墩底比墩身中部和墩顶更容易发生破坏。龙江等[7]基于增量动力分析（incremental dynamic analysis，IDA）方法探究连续梁桥地震易损性，结果表明隔震桥墩损伤概率与墩高密切相关，墩高越高，墩顶位移越大，桥墩损伤概率也越大。HWANG等[8-9]针对桥墩发生弯曲破坏时，提出采用位移延性比定义桥梁墩柱的损伤。KARIM等[10]通过数值模拟提出构建桥墩易损性曲线的方法，并与由阪神地震得到的经验易损性曲线进行对比，验证其可行性。张菊辉[11]基于数值模拟的一种建立地震易损性曲线的分析方法，并对规则梁桥的墩柱在纵横向输入下分别进行易损性研究，探讨墩高、箍筋配箍率的变化对易损性曲线的影响。
综上所述，可以看出现有的研究多数只对变墩高曲线桥墩柱在压弯耦合荷载作用下进行了易损性分析，但在实际工程中墩柱偏心支承时的变墩高小半径曲线桥在地震作用下往往会呈现出压弯剪扭耦合的复杂空间受力状态，可见对扭转造成的曲线桥桥墩地震损伤研究是十分必要的。因此亟需开展相关研究确定，在考虑扭转作用下，曲线桥的地震损伤破坏规律。
基于上述分析，利用SeismoStruct有限元平台建立考虑桥墩受压弯剪扭多种耦合作用的有限元模型，以曲线桥的桥墩为研究对象，提出扭转破坏模式下桥墩的损伤指标，探究不同布置形式、损伤指标对于变墩高曲线桥桥墩地震易损性的影响。
1　桥梁模型建立
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1.1　桥梁原型
在城市中跨主干线路的小半径曲线桥通常因被交通道路的通行限制而需设置较大偏心的桥墩，因此相当于额外施加扭转的桥墩在地震作用下可能会产生扭转破坏，如图1所示。为探究偏心支承墩柱小半径曲线桥的地震易损性，本文选取某互通式立交匝道桥的第2联为工程背景。该匝道桥为4 × 20 m预应力混凝土等截面曲线连续箱梁桥，圆心角为92°，曲率半径为50 m，箱梁宽8.5 m，高2 m，腹板厚60 cm，采用C50混凝土浇筑。其下部结构共有5个桥墩，中间3个桥墩（1、2、3号墩）为直径2 m的钢筋混凝土圆形截面独柱墩，布置形式为渐变型，高度依次为15、12、9 m，其中将M墩沿68°方向偏移5.4 m布置。两侧的过渡墩（0、4号墩）为直径1.3 m、高9 m的双柱墩，边、中墩均采用C30混凝土浇筑。上部结构与下部结构采用支座连接，中间墩采用固定盆式支座，支座型号为GPZ（KZ）9GD，过渡墩采用单向滑动支座（顺桥向滑动、横桥向固定），支座型号为GYZF4 200×44 mm。桥梁结构示意图与主梁截面示意图如图2、图3所示。
1.2　数值分析模型
本文基于SeismoStruct有限元软件建立了2种不同布置形式的变墩高小半径曲线桥，各布置形式下桥墩高度具体如表1所示。本次变墩高设计中，桥墩高度共包括15、12、9 m这3种。为了方便统计，15 m墩简称为H（High）墩，12 m墩简称为M（Medium）墩，9 m墩简称S（Short）墩。
压弯剪扭耦合受力构件的模拟方法及实验验证如下所述。
1）集中铰-纤维模型模拟压弯剪扭耦合受力构件
COLEMAN等[12]研究发现，传统的纤维模型虽然可以很好地模拟桥墩的弯曲效应，但存在应变局部化问题。李剑等[13]用纤维模型模拟墩柱会高估其弯曲耗能能力，无法准确考虑刚度退化、强度退化等方面对桥墩抗震性能的影响，特别是在考虑压弯剪扭耦合作用下，无法准确评估桥墩的非线性力学损伤行为。MOVAGHATI等[14]为精确模拟桥墩在地震作用下的真实行为提出集中铰-纤维模型，在传统的纤维模型基础上通过串联非线性弹簧考虑压弯剪扭耦合效应的一种新模型单元。考虑剪切效应和扭转效应的集中铰-纤维模型能够更好地预测桥墩的抗震性能，最大程度地反映墩柱的强度退化、刚度退化及耗能能力，因此更适用于耦合受力墩柱的模拟[15]。本文采用集中铰-纤维模型模拟桥墩，其中混凝土采用Mander本构模型，钢筋采用Menegotto-Pinto本构模型。对桥墩添加零长度弹簧单元，如图4所示。采用Takeda模型来模拟定义桥墩的剪切恢复力模型，当桥墩受到较大的剪切作用时，桥墩中部会出现一定倾斜角度的斜裂缝，从而导致桥墩刚度以及延性的降低，因此需要在桥墩中部添加剪切弹簧来模拟刚度的降低；采用Multi-linear curve模型来模拟其恢复受到的扭转作用[16]，当桥墩受到较大扭转作用时，在墩顶与盖梁交界处会出现较大的扭转损伤，因此在桥墩顶部添加扭转弹簧能够模拟扭转效应对于桥墩扭转刚度及抗扭承载力带来的影响。屈服力参考文献[13]计算压剪扭耦合受力钢筋混凝土墩柱的抗剪承载力和抗扭承载力，其他各参数取值参照文献[17]。焦驰宇等[18]进行的压弯剪扭耦合受力桥墩的拟静力试验与考虑剪切扭转弹簧单元的恢复力模型进行了对比分析。
2）全桥其他构件的三维有限元建模
在SeismoStruct建模过程中，主梁采用弹性梁单元模拟，桥墩采用集中铰-纤维模型模拟。支座采用六自由弹簧单元模拟，边墩滑动支座的本构关系按照JTG/T 2231-01—2020《公路桥梁抗震设计规范》[19]规定在非线性分析中采用双线性理想弹塑性模拟，其中滑动摩擦系数μ取0.02，支座屈服位移xy取0.002 m。中间墩（1、2、3号墩）固定支座采用弹簧模拟，轴向采用大刚度模拟，只允许转动，不允许平动，具体参数参照文献[9]，有限元模型如图5所示。
2　易损性分析方法
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地震易损性分析是指在特定的地震动强度下，结构处于不同损伤状态的概率，可用式（1）进行表示：
式中：Pf为结构或构件的失效概率；D为结构的地震响应；C为损伤极限状态；IM为地震动强度参数；X为指定的地震动强度水平。
本文采用能力需求比模型的曲线拟合法[20]建立曲线桥的理论易损性曲线，可有效降低易损性曲线参数回归时的离散性，更具有客观性[18]。具体过程如式（2）~式（4）所示：
式中：n为样本个数；Sr为回归的残差平方和；a、b、c为拟合参数；μd为需求位移延性比；μc为能力位移延性比；μ为PGA逐渐增大所对应的期望；σ为拟合标准差；Pf为完全损伤的超越概率。
3　基于易损性的抗震性能评估
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3.1　地震波选取
桥梁所处场地参数抗震设防烈度为8度，加速度峰值为0.3 g，设计地震分组第1组，场地条件Ⅲ类。根据目标反应谱，从太平洋地震工程研究中心（Pacific Earthquake Engineering Research Center，PEER）数据库中选取符合Ⅲ类场地特性的50条地震波，所选地震波的频谱特性及其场地规范反应谱对比如图6所示。由图可知，本次的地震记录选取较为合理。
3.2　极限状态量化与强度指标选取
由于曲线桥在地震作用下还会受到扭转作用的影响，当扭转效应增大到一定程度时，桥墩甚至会产生以扭转为主的损伤破坏，因此在对偏心支承墩柱小半径曲线桥地震易损性分析之前，先判别桥墩的破坏模式[21]，由此采用扭转角延性比作为损伤指标划分桥墩的扭转损伤等级，其计算公式为
式中：μθ为扭转角延性比；θT为扭转角；θc为桥墩混凝土开裂时的扭转角。
结合恒载受力下桥墩结构及相关配筋情况，同时借鉴文献[21]中的公式分别计算桥墩的极限位移延性比与极限扭转角延性比，判断地震作用下该桥墩是先达到极限位移延性比还是极限扭转角延性比即可得到桥墩的破坏模式。
以Kern County地震为例，图7给出了2种布置形式下M墩的破坏模式判别结果。由图可知，M墩在1.2 g下达到了极限位移延性比，在1.0 g下就已经达到了极限扭转角延性比。因此，桥墩将首先发生扭转破坏。
扭转损伤破坏的主要发展趋势为多条交叉裂缝发展形成主裂缝最终到混凝土剥落，具体如图8所示。基于此，将桥墩的扭转破坏划分为无损伤、轻微损伤、中等损伤和完全损伤4个等级，各损伤状态的描述如表2所示。
基于扭转破坏桥墩损伤划分，引入桥墩扭转-扭矩骨架曲线，将其等效为三线性简化曲线，如图9所示。根据计算式（6）~式（11）分别计算[16，21]扭转骨架曲线上各特征点的数值，并以此为限值来划分各等级损伤状态，具体如表3所示。
式中：Tc为开裂扭矩；为构件抗扭承载力降低系数；βt为压弯剪扭耦合受力下，考虑剪扭影响的混凝土抗扭承载力降低系数；ft为混凝土抗拉强度；Wt为截面受扭抵抗矩；Leff为有效高度；G为混凝土剪切模量；εy为屈服扭矩对应的箍筋应变；Ty为最大峰值屈服扭矩；fyv为箍筋屈服强度；ζ′为纵筋与箍筋强度比值；Astl为单肢箍筋截面面积；Tu为极限扭矩；θu为极限转角；Lpv为扭转塑性铰长度，取1.1d；εu为极限扭矩对应的箍筋应变。
4　桥墩易损性曲线分析
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1）损伤指标影响
为了探究不同损伤指标对于扭转破坏桥墩易损性的影响，图10给出了渐变型下分别采用弯曲破坏损伤指标与扭转损伤指标绘制的M墩轻微损伤与完全损伤易损性曲线的对比。由图可知，与完全损伤相比，两者的轻微损伤易损性曲线较为接近，最大差值仅为5%，但弯曲破坏主要发生在墩底，扭转破坏主要发生在墩身。而对于完全损伤来讲，以扭转损伤作为指标，M墩在完全损伤的概率要增大16.7%。从损伤状态的描述上来分析，不论是弯曲损伤指标还是扭转损伤指标在定义轻微破坏时均以混凝土多条裂缝的出现为发生轻微损伤的判别条件，因此对应的轻微损伤易损性曲线差异不大。然而在定义完全损伤时，扭转损伤指标以混凝土大块剥落为判别条件，弯曲损伤指标以核心混凝土压碎为界限。这也说明，对于扭转破坏型桥墩，如果采用弯曲损伤指标来划分损伤状态对于轻微破坏的概率影响不大，但是会低估桥墩在强震下发生失效的概率。
综上所述，为了后续的简化分析，本文对M墩以扭转破坏作为损伤破坏指标进行易损性分析，其他墩柱仍以弯曲破坏作为损伤破坏指标进行易损性分析。后续据此展开深入分析。
2）布置形式影响
依据相关文献[17]，相比于凸岛型，渐变型与凹岛型的易损性差异更大。由此按照理论易损性曲线的建立方法分别绘制了渐变型与凹岛型的M墩在不同损伤状态下的易损性曲线，如图11所示。由图可知，2种布置形式下的易损性曲线基本符合随着地震动强度的增加，结构的损伤超越概率逐渐增大。在同一地震动强度水平下，发生从轻微到完全损伤的超越概率逐渐降低。其中，中等损伤与完全损伤的超越概率较为接近，且要远低于轻微损伤。从易损性曲线线型上来看，随着PGA的逐级增加，各损伤状态的易损性曲线增速都较为均匀，中等损伤曲线整个过程中未出现增速缓点。其中渐变型下，M墩在PGA为1.2 g时，轻微损伤的超越概率增长至85%，中等损伤与完全破坏的超越概率分别增长至34%、20%。凹岛型下M墩在PGA为1.2 g时，轻微损伤的超越概率增长至86%，中等损伤与完全损伤的超越概率分别增长至45%、31%。
为了进一步对比不同布置形式对于桥墩扭转易损性的影响，图12给出了2种布置形式下各损伤状态的易损性曲线对比。由图可知，不同布置形式下，桥墩的轻微损伤曲线的最大差值在0.5 g时达到了5.7%。对于中等损伤以及完全损伤，两者的差值在PGA为1.2 g时分别达到了最大值11.6%与11.7%。由此可以看出，对于发生扭转破坏的偏心桥墩来讲，变墩高形式主要影响了中等损伤以及完全损伤的超越概率，并且凹岛型下桥墩的损伤超越概率要大于渐变型。由于凹岛型布置形式下曲线桥的扭转刚度最小[16]，在地震作用下主梁会产生更加强烈的扭转效果，导致对于偏心桥墩施加的附加扭转更大，使得桥墩产生更严重的扭转破坏。
5　结论
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本文基于偏心支承小半径曲线桥的桥墩，考虑变墩高曲线桥的桥墩承受耦合作用的情况，开展了渐变型、凹岛型布置形式下桥墩的地震易损性分析，得出以下结论：
1）当曲线桥的墩柱偏心设置时，凹岛型曲线桥的墩柱在各损伤状态的超越概率要大于渐变型。由于变墩高带来的刚度差异，因而将产生更严重的扭转破坏，因此在抗震设计中应尽可能避免凹岛型布置形式。
2）无论是渐变型还是凹岛型2种布置形式都符合随着地震动强度的增加，结构的损伤超越概率逐渐增大。但对于发生扭转损伤的桥墩，变墩高形式主要影响墩柱发生中等损伤及完全损伤的超越概率，而对轻微损伤的影响较小。
3）对于以扭转为主损伤的桥墩，不同布置形式对于桥墩的易损性影响与地震动强度、桥墩高度等都有一定联系。采用弯曲损伤指标来划分损伤状态虽然对于轻微损伤的概率影响不大，但是对偏心支承曲线桥往往由于忽略扭转损伤的存在，会低估桥墩在强震下损伤失效概率。
基金
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  • 国家自然科学基金项目(52078023; 52378472)
  • 北京市自然科学基金-北京市教委联合重点项目(23JH0014)
  • 北京建筑大学建大领军人才计划B类项目(JDLJ20220807)
  • 北京市博士后工作经费资助项目(2023-zz-137)
文献
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2025年第45卷第2期
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文章信息
doi: 10.13197/j.eeed.2025.0209
  • 接收时间：2024-03-13
  • 首发时间：2026-03-20
  • 出版时间：2025-04-24
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文章信息
作者
出版历史
  • 收稿日期：2024-03-13
  • 修回日期：2024-05-12
基金
国家自然科学基金项目(52078023; 52378472)
北京市自然科学基金-北京市教委联合重点项目(23JH0014)
北京建筑大学建大领军人才计划B类项目(JDLJ20220807)
北京市博士后工作经费资助项目(2023-zz-137)
作者信息
    1.北京市城市交通基础设施建设工程技术研究中心，北京 100044
    2.北京建筑大学 工程结构与新材料北京市高等学校工程研究中心，北京 100044
    3.北京建筑大学古桥研究院，北京 100044
    4.北京工业大学 城市与工程安全减灾教育部重点实验室，北京 100124
    5.北京建筑大学大型多功能振动台阵实验室，北京 100044
    6.中恒工程设计院有限公司，四川 成都 610017

通讯作者:

方蓉（1991—），女，博士，主要从事桥梁抗震研究。E-mail：
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https://castjournals.cast.org.cn/joweb/dzgcygczd/CN/10.13197/j.eeed.2025.0209
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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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