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Article(id=1245373263963078989, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245373256329441426, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0114, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1665072000000, receivedDateStr=2022-10-07, revisedDate=1679241600000, revisedDateStr=2023-03-20, acceptedDate=null, acceptedDateStr=null, onlineDate=1774849724045, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774849724045, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774849724045, creator=13701087609, updateTime=1774849724045, updator=13701087609, issue=Issue{id=1245373256329441426, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='1', pageStart='1', pageEnd='236', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774849722225, creator=13701087609, updateTime=1774851286407, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245379817042981204, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245373256329441426, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245379817042981205, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245373256329441426, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=148, endPage=157, ext={EN=ArticleExt(id=1245373264386703720, articleId=1245373263963078989, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Study on the influence of the layout of isolation bearings on the seismic performance of stilted buildings on the slope, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In this paper, the stilted buildings were taken as the research object, and according to the characteristics of unequal height embedded structure, three types of three-dimensional stilted frame structures were designed: non-isolation, base isolation and the second floor column bottom isolation (interlayer isolation). Then elastic response spectrum analysis and elastic-plastic dynamic time history analysis of analysis models were carried out to investigate the influence of different isolation bearing layout on the dynamic response, failure mode, probability of seismic collapse and other seismic performance of stilted frame structures. The results show that the application of seismic isolation technology to the stilted frame structure on slope can control the dynamic response of the structure and improve the safety margin of the whole structure, which provides a new way to improve its seismic performance. The setting of base isolation can improve the non-uniformity of structural stiffness distribution, reduce the difference of shear distribution between stilted columns and improve the safety reserve of the shortest columns. However, there are differences in the deformation of isolation bearings with different levels. Isolation bearings with different lateral stiffness should be arranged in the base isolation model. Compared with the base isolation, the interlayer isolation has better ability to control the structural damage, the deformation of the upper floor is more uniform, and the probability of seismic collapse is lower. However, in the interlayer isolation design, it should be considered to appropriately reduce the difference of lateral stiffness between stilted columns.

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以坡地吊脚楼为研究对象，针对结构不等高嵌固的特点，分别设计了无隔震、基础隔震和第二层柱底隔震（层间隔震）这3种三维吊脚框架结构算例。开展算例模型的弹性反应谱分析和弹塑性动力时程分析，考察隔震支座布置形式对吊脚框架结构动力响应、破坏模式以及地震倒塌概率等抗震性能的影响规律。结果表明：将隔震技术运用于坡地吊脚框架结构中可以控制结构动力响应，为改善吊脚框架结构抗震性能提供了新途径；设置基础隔震可改善结构刚度分布的不均匀性，降低吊脚柱之间剪力差异，提高吊脚短柱安全储备，但不同标高处隔震支座的变形存在差异；与基础隔震相比，层间隔震对结构损伤控制的能力更优，层间隔震模型上部楼层变形更为均匀，地震倒塌概率更低，但在层间隔震结构设计中应考虑适当减小吊脚柱间侧向刚度的差异。

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刘立平（1971—），男，教授，博士，主要从事结构抗震分析及设计理论研究。E-mail：
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李瑞锋（1995—），男，博士研究生，主要从事山地建筑结构抗震性能研究。E-mail：

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李瑞锋（1995—），男，博士研究生，主要从事山地建筑结构抗震性能研究。E-mail：

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李瑞锋（1995—），男，博士研究生，主要从事山地建筑结构抗震性能研究。E-mail：

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ArticleFig(id=1245373275136705473, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245373263963078989, language=CN, label=图14, caption=倒塌概率易损性曲线, figureFileSmall=jeVaYzLK9HMkQ89aBqJPXQ==, figureFileBig=FwV1h9ZTx1GZfdW6XrDDAA==, tableContent=null), ArticleFig(id=1245373275241563076, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245373263963078989, language=EN, label=Table 1, caption=

Performance parameters of isolation bearing

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性能参数性能值
剪切模量/MPa0.392
等效水平刚度/（kN/m）1325
等效阻尼比/%27.2
屈服后刚度/（kN/m）715
屈服力/kN41.9
), ArticleFig(id=1245373275342226378, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245373263963078989, language=CN, label=表1, caption=

隔震支座性能参数

, figureFileSmall=null, figureFileBig=null, tableContent=
性能参数性能值
剪切模量/MPa0.392
等效水平刚度/（kN/m）1325
等效阻尼比/%27.2
屈服后刚度/（kN/m）715
屈服力/kN41.9
), ArticleFig(id=1245373275484832718, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245373263963078989, language=EN, label=Table 2, caption=

Results of modal analysis

, figureFileSmall=null, figureFileBig=null, tableContent=
模型阶数周期/s方向模型阶数周期/s方向
M1-1一阶0.97XM2-1一阶0.84X
二阶0.97Y二阶0.81Y
三阶0.83R三阶0.72R
M1-2一阶2.38YM2-2一阶2.16Y
二阶2.29X二阶2.11X
三阶1.97R三阶1.84R
M1-3一阶1.96XM2-3一阶1.92X
二阶1.96Y二阶1.91Y
三阶1.76R三阶1.72R
), ArticleFig(id=1245373275577107412, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245373263963078989, language=CN, label=表2, caption=

模态分析结果

, figureFileSmall=null, figureFileBig=null, tableContent=
模型阶数周期/s方向模型阶数周期/s方向
M1-1一阶0.97XM2-1一阶0.84X
二阶0.97Y二阶0.81Y
三阶0.83R三阶0.72R
M1-2一阶2.38YM2-2一阶2.16Y
二阶2.29X二阶2.11X
三阶1.97R三阶1.84R
M1-3一阶1.96XM2-3一阶1.92X
二阶1.96Y二阶1.91Y
三阶1.76R三阶1.72R
), ArticleFig(id=1245373275690353622, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245373263963078989, language=EN, label=Table 3, caption=

Results of collapse probability under rare and extreme rare earthquakes

, figureFileSmall=null, figureFileBig=null, tableContent=
结构失效部位罕遇地震（400 cm/s2）极罕遇地震（700 cm/s2）
无隔震-RC框架0.190.49
基础隔震-RC框架0.160.45
层间隔震-RC框架0.040.18
基础隔震-隔震装置0.150.40
层间隔震-隔震装置0.080.30
), ArticleFig(id=1245373275795211224, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245373263963078989, language=CN, label=表3, caption=

罕遇、极罕遇地震下模型倒塌概率结果

, figureFileSmall=null, figureFileBig=null, tableContent=
结构失效部位罕遇地震（400 cm/s2）极罕遇地震（700 cm/s2）
无隔震-RC框架0.190.49
基础隔震-RC框架0.160.45
层间隔震-RC框架0.040.18
基础隔震-隔震装置0.150.40
层间隔震-隔震装置0.080.30
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隔震支座布置形式对坡地吊脚楼结构抗震性能的影响研究
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李瑞锋 1, 2 , 刘立平 1, 2 , 尹力 1 , 韩树旺 1 , 李英民 1, 2
地震工程与工程振动 | 2024,44(1): 148-157
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地震工程与工程振动 | 2024, 44(1): 148-157
隔震支座布置形式对坡地吊脚楼结构抗震性能的影响研究
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李瑞锋1, 2 , 刘立平1, 2 , 尹力1, 韩树旺1, 李英民1, 2
作者信息
  • 1.重庆大学 土木工程学院，重庆 400045
  • 2.重庆大学 工程结构抗震防灾重庆市重点实验室，重庆 400045

    • 李瑞锋（1995—），男，博士研究生，主要从事山地建筑结构抗震性能研究。E-mail：

通讯作者:

刘立平（1971—），男，教授，博士，主要从事结构抗震分析及设计理论研究。E-mail：
Study on the influence of the layout of isolation bearings on the seismic performance of stilted buildings on the slope
Ruifeng LI1, 2 , Liping LIU1, 2 , Li YIN1, Shuwang HAN1, Yingmin LI1, 2
Affiliations
  • 1.College of Civil Engineering, Chongqing University, Chongqing 400045, China
  • 2.Key Laboratory of Earthquake Resistance and Disaster Prevention for Engineering Structures, Chongqing University, Chongqing 400045, China
doi: 10.13197/j.eeed.2024.0114
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摘要
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以坡地吊脚楼为研究对象，针对结构不等高嵌固的特点，分别设计了无隔震、基础隔震和第二层柱底隔震（层间隔震）这3种三维吊脚框架结构算例。开展算例模型的弹性反应谱分析和弹塑性动力时程分析，考察隔震支座布置形式对吊脚框架结构动力响应、破坏模式以及地震倒塌概率等抗震性能的影响规律。结果表明：将隔震技术运用于坡地吊脚框架结构中可以控制结构动力响应，为改善吊脚框架结构抗震性能提供了新途径；设置基础隔震可改善结构刚度分布的不均匀性，降低吊脚柱之间剪力差异，提高吊脚短柱安全储备，但不同标高处隔震支座的变形存在差异；与基础隔震相比，层间隔震对结构损伤控制的能力更优，层间隔震模型上部楼层变形更为均匀，地震倒塌概率更低，但在层间隔震结构设计中应考虑适当减小吊脚柱间侧向刚度的差异。

吊脚框架结构  /  隔震支座  /  抗震性能  /  动力响应  /  地震倒塌概率

In this paper, the stilted buildings were taken as the research object, and according to the characteristics of unequal height embedded structure, three types of three-dimensional stilted frame structures were designed: non-isolation, base isolation and the second floor column bottom isolation (interlayer isolation). Then elastic response spectrum analysis and elastic-plastic dynamic time history analysis of analysis models were carried out to investigate the influence of different isolation bearing layout on the dynamic response, failure mode, probability of seismic collapse and other seismic performance of stilted frame structures. The results show that the application of seismic isolation technology to the stilted frame structure on slope can control the dynamic response of the structure and improve the safety margin of the whole structure, which provides a new way to improve its seismic performance. The setting of base isolation can improve the non-uniformity of structural stiffness distribution, reduce the difference of shear distribution between stilted columns and improve the safety reserve of the shortest columns. However, there are differences in the deformation of isolation bearings with different levels. Isolation bearings with different lateral stiffness should be arranged in the base isolation model. Compared with the base isolation, the interlayer isolation has better ability to control the structural damage, the deformation of the upper floor is more uniform, and the probability of seismic collapse is lower. However, in the interlayer isolation design, it should be considered to appropriately reduce the difference of lateral stiffness between stilted columns.

stilted frame structures  /  isolation bearings  /  seismic behavior  /  dynamic response  /  probability of seismic collapse
李瑞锋, 刘立平, 尹力, 韩树旺, 李英民. 隔震支座布置形式对坡地吊脚楼结构抗震性能的影响研究. 地震工程与工程振动, 2024 , 44 (1) : 148 -157 . DOI: 10.13197/j.eeed.2024.0114
Ruifeng LI, Liping LIU, Li YIN, Shuwang HAN, Yingmin LI. Study on the influence of the layout of isolation bearings on the seismic performance of stilted buildings on the slope[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (1) : 148 -157 . DOI: 10.13197/j.eeed.2024.0114
正文
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0　引言
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因对边坡的良好适应性，坡地建筑结构在山地城镇建设中得到广泛应用。吊脚框架结构是坡地建筑中常见的结构形式之一，其结构特点是沿边坡布置不等高的接地柱，在地震作用下，吊脚层的水平力与损伤将集中于坡上的吊脚短柱，导致结构局部破坏严重，难以实现最长失效路径，不能充分发挥结构的变形与耗能能力，降低了结构的抗震安全裕度。历次山地地震的震害也表明，相较于普通平地结构，吊脚框架结构遭受到了更为严重的损伤，出现更高的倒塌概率[1-3]。
近年来，国内外学者对吊脚框架结构的抗震性能开展了系列研究。其中，SURANA等[4]分析了印度山区吊脚框架结构的构造特点和地震破坏形态，研究表明吊脚短柱是该类结构的薄弱部位。杨实君[5]对吊脚框架结构采用Push-Over方法进行抗震性能分析，研究发现相比于普通平地框架结构，吊脚框架结构的顺坡向延性较差。秦晨[6]采用数值模拟方法，研究了吊脚框架结构在大震下的构件内力与破坏形态，发现吊脚层框架梁将承担较大的轴力，设计时宜考虑梁轴力的影响。刘立平等[7]开展了一榀吊脚框架的拟静力试验，研究发现底部吊脚层各柱间抗侧刚度的不均性导致吊脚柱损伤程度存在差异，吊脚短柱的下端及与其相邻的梁端破坏最为严重。为提升结构抗震性能，宜减小各吊脚柱之间抗侧刚度的不均匀程度。
设置隔震支座可延长结构周期，降低结构的地震响应与破坏程度，是一种提升结构抗震性能的有效技术手段。众多学者已对平地隔震结构的抗震性能开展了大量研究，验证了其有效性[8-10]。但对于隔震技术在坡地建筑结构中的研究还相对较少。目前，部分学者对设置隔震支座的坡地掉层框架结构的抗震性能开展了研究。其中，韩军等[11]通过数值模拟方法考察了基础隔震掉层框架结构的抗震性能，研究发现在上接地层柱底设置隔震支座将导致薄弱楼层转移至掉层部分，其宜设置在掉层跨数较多的结构中。张龙飞等[12]开展了设置隔震支座的掉层框架结构地震模拟振动台试验，该研究通过在上下接地部分设置隔震支座，形成掉层隔震结构，发现与无隔震的结构相比，设置隔震支座可提高结构的安全裕度，同时结构的扭转效应也得到控制，验证了隔震技术在掉层结构中的可行性。但上述研究的对象均为坡地掉层结构，还未见隔震技术在坡地吊脚框架结构中的研究与应用。
吊脚框架结构底部不等高嵌固的特征导致其隔震布置与普通平地结构存在差异，本文针对结构不等高嵌固的特点，分别设计了无隔震、基础隔震和第二层柱底隔震（层间隔震）3种吊脚框架结构算例。利用SAP2000有限元软件建立结构算例的有限元分析模型，开展弹性反应谱分析和弹塑性动力时程分析，考察隔震支座布置形式对吊脚框架结构地震响应、破坏模式以及倒塌概率等抗震性能的影响规律。
1　吊脚框架结构模型设计
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坡地吊脚框架结构沿边坡布置不等高的接地柱，受坡度以及吊脚短柱长度影响，结构吊脚层的侧向刚度可具有较大变化范围。且其侧向刚度将影响结构的层间变形以及大震下的破坏形态，是影响结构抗震性态的关键因素之一。为充分考察隔震支座布置形式对吊脚结构抗震性能的影响，本文设计了2个吊脚框架结构，模型设计原则为吊脚层的侧向刚度不同，上部楼层侧向刚度保持一致。将吊脚层侧向刚度较小的结构命名为M1-1，侧向刚度较大的结构命名为M2-1。2个结构平面布置均为2×3跨（顺坡向2跨，横坡向3跨），层数为7层，结构梁截面尺寸均为300 mm×450 mm，第二到第七层柱截面尺寸均为450 mm×450 mm，M1-1吊脚层柱截面尺寸为480 mm×480 mm，M2-1的为750 mm×750 mm，结构顺坡向几何尺寸如图1（a）所示。结构主要设计参数为：抗震设防烈度为8度0.2 g，场地类别为二类，框架抗震等级为2级。结构楼面附加恒载为1.5 kN/m2，附加活载为2 kN/m2。屋面附加恒载为4 kN/m2，附加活载为0.5 kN/m2。混凝土强度等级为C30级，钢筋强度等级为HRB400级。
考虑吊脚结构不等高接地的特点，针对设计的2个不同吊脚层侧向刚度的结构模型，分别采用基础隔震布置形式与层间隔震布置形式，设计了4个吊脚隔震模型，如图1（b）、（c）。其中模型M1-2、M1-3对应无隔震模型M1-1，模型M2-2、M2-3对应无隔震模型M2-1。基础隔震模型为在吊脚柱底端设置隔震支座，因此隔震支座不可避免地具有不等高布置的特点。层间隔震为在吊脚层相邻上一层设置隔震层，该隔震层高度为1 m。在层间隔震模型中，隔震支座布置于相同标高处，具有变形协同的特点，但吊脚层仍具有刚度分布的不均匀性。隔震模型均采用LRB400型铅芯橡胶支座[13]，其布置如图1（b）、（c）所示，主要力学性能参数如表1所示。依据现行的抗震设计规范对6个模型进行配筋设计[14]。
利用SAP2000软件建立结构算例的有限元分析模型，采用集中塑性铰模型考虑结构非线性行为，塑性铰参数依据FEMA356[15]的默认参数进行设置。对设计的6个模型开展模态分析，得到各模型前3阶振型对应的周期以及振型方向，模态分析结果如表2所示。由表可知，设置隔震支座后模型自振周期相较于无隔震模型的有所延长，同时设置层间隔震对周期延长的效果是小于设置基础隔震的。
2　多遇地震下弹性分析结果
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对6个模型结构开展顺坡向的弹性反应谱分析，得到吊脚隔震模型和无隔震模型的层间位移、层剪力和吊脚柱剪力，考察多遇地震下2种隔震支座布置形式对结构弹性地震响应的影响。
弹性反应谱分析所得各模型顺坡向的层间剪力如图2所示。由图可知，设置基础隔震与层间隔震均可有效减小吊脚结构各楼层的剪力需求，其中设置基础隔震对减小结构层剪力需求的作用稍强于层间隔震。各模型的层间位移角如图3所示，图中基础隔震模型第一层的层间位移角对应吊脚短柱上下端的位移差，层间隔震模型第二层的层间位移，未包括隔震层的位移。由图3可知，吊脚层间隔震模型各楼层的层间位移均小于无隔震模型的，表明其可有效降低结构位移响应。吊脚基础隔震模型第三层以上楼层的层间位移角明显小于无隔震模型的，但吊脚层及其上一层的层间位移角接近或大于无隔震模型的，其主要原因是设置基础隔震后改变了吊脚柱底端的约束形式，降低了吊脚柱侧向刚度，使得下部楼层位移需求有所增加。
弹性反应谱分析所得各模型顺坡向中榀框架吊脚柱的剪力值如图4所示。由图可知，在吊脚柱截面尺寸相同的情况下，因吊脚层柱间刚度分布的不均匀性，无隔震模型吊脚柱的剪力分布呈现显著的不均匀性，其集中于吊脚短柱。相较于无隔震模型与层间隔震模型，基础隔震模型吊脚层各柱间剪力分布的不均匀程度降低，表明设置基础隔震模型可改善吊脚层各柱刚度分布的不均匀性。设置层间隔震未改变吊脚结构底部侧向刚度分布，其吊脚层各柱剪力分布也具有不均匀性，但层间隔震降低了整体结构的地震响应，该模型吊脚短柱的抗剪需求也相应减小。
3　罕遇地震弹塑性分析结果
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选用2条天然地震波和1条人工地震波，对6个模型开展弹塑性动力时程分析。地震动作用方向为顺坡向，3条地震波反应谱（0.05阻尼比）与规范反应谱对比如图5所示。依据建筑抗震规范，罕遇地震分析中地震动加速度峰值调整至400 cm/s2，阻尼比取为0.05。通过对比分析吊脚结构模型的层间位移、构件内力和破坏形态等地震响应，考察2种隔震支座布置形式对罕遇地震作用下吊脚结构抗震性能的影响。
3.1　破坏形态
罕遇地震作用下无隔震模型顺坡向中榀框架的塑性铰分布如图6所示。由图可知，无隔震模型损伤较为严重，在3条地震动作用下，不同吊脚层侧向刚度模型（M1-1和M2-1）的大部分楼层梁端和底部楼层柱端均出现塑性铰。因吊脚层侧向刚度的差异，模型M1-1和M2-1柱端塑性铰出现的部位不一致。对于吊脚层侧向刚度较小的模型M1-1，柱端塑性铰主要出现在吊脚短柱以及第二层柱下端。吊脚层各柱刚度分布的不均匀导致吊脚短柱下端塑性铰出现时间较早、发育程度较充分。因吊脚短柱是结构主要的承重构件，其严重破坏将影响整体结构的抗震安全性。因此对于吊脚层侧向刚度较小的吊脚结构，大震下其吊脚层可能出现较大程度破坏，导致吊脚短柱出现严重损伤，影响结构抗震安全性。对于吊脚层侧向刚度较大的模型M2-1，柱端塑性铰出现在第二层柱下端，其主要原因是结构底部层间刚度分布的不均匀性导致结构变形与损伤集中于吊脚层以上楼层。
由图7的基础隔震模型顺坡向中榀框架塑性铰分布图可知，设置基础隔震后，结构的破坏程度相对于无隔震模型明显减轻，其梁端塑性铰仅出现在下部3层。对于模型M2-2，其仅在人工波和Chi-Chi波作用下第二层中柱顶端出现柱端塑性铰。对于模型M1-2，其在人工波和Chi-Chi波作用下分别于吊脚长柱与中柱上端出现柱端塑性铰，主要原因可能在于设置隔震后吊脚层刚度的改变以及吊脚层的隔震支座布置于不同标高处，导致吊脚柱的变形不协调。
由图8的层间隔震模型顺坡向中榀框架塑性铰分布图可知，模型结构的塑性铰仅出现在梁端，且梁端塑性铰出现的数量也明显小于基础隔震模型，表明相较于基础隔震，设置层间隔震对结构破坏程度控制的能力更优。但对于吊脚层侧向刚度较小的模型M1-3，其吊脚层与吊脚短柱相连的梁端在3条地震波作用下均出现塑性铰，其破坏可能会影响隔震支座的正常工作。因此对于吊脚层刚度较小的结构，在设置层间隔震时，宜对靠近吊脚短柱的梁端进行适当抗震加强。
3.2　层间位移角
罕遇地震下模型M1-1、M1-2、M1-3及模型M2-1、M2-2、M2-3顺坡向中榀框架层间位移角峰值随楼层的分布如图9、图10所示。由图可知，基础隔震模型第三层及以上楼层的层间位移角峰值是明显小于无隔震模型的，表明设置基础隔震可有效减轻上部楼层在罕遇地震作用下的位移响应，从而减轻上部楼层的损伤。其中对于吊脚层侧向刚度较小的模型，在人工波作用下，第一、二层的层间位移角均大于无隔震模型的。对于吊脚层侧向刚度较大的模型，在人工波以及2条天然波作用下，其第一、二层的层间位移角均大于无隔震模型的。主要原因在于设置基础隔震后吊脚层底部约束的改变，最大层间位移角出现于基础隔震模型底部吊脚层处。由图7可知，基础隔震模型的塑性铰也集中出现于吊脚层及其相邻上一层，因此在基础隔震模型设计中应控制吊脚层的侧向位移，避免结构吊脚层以及其相邻上一层出现过大的层间位移。
由图9、图10可知，层间隔震模型各楼层的层间位移角峰值均显著小于无隔震模型，其中在人工波作用下模型M1-3的最大层位移角为模型M1-1的45%，模型M2-3的最大层位移角为模型M2-1的35%，表明设置层间隔震可有效控制结构的位移响应。同时，层间隔震模型上部楼层层间位移角随楼层的分布相比无隔震模型以及基础隔震模型的更为均匀，避免侧向变形集中于局部楼层。
3.3　隔震支座变形
在基础隔震模型中，沿边坡布置的隔震支座不可避免地具有不等高布置的特征，在地震作用下，不同高度处的隔震支座变形可能不相等。为考察基础隔震模型中隔震支座的变形规律，将人工波作用下基础隔震模型（M1-2、M2-2）顺坡向中榀框架沿边坡布置的3个隔震支座侧向变形以及层间隔震模型（M1-3、M2-3）隔震支座变形如图11所示。图中，基础隔震长柱、基础隔震中柱和基础隔震短柱分别为基础隔震模型吊脚长柱、中柱以及短柱下端布置的隔震支座。由图11可知，2个不同吊脚层侧向刚度的基础隔震模型支座的侧向变形具有相同的规律，均为吊脚短柱下端隔震支座具有最大的侧向变形，其次为吊脚中柱处的支座，吊脚长柱处的隔震支座的侧向变形最小。其主要原因是结构的不等高嵌固导致吊脚柱的剪力分配具有不均匀性，剪力最大的吊脚短柱下端的隔震支座具有最大的变形需求。在边坡下方的隔震支座的最大变形明显小于层间隔震支座，导致边坡下方的隔震支座不能充分发挥其耗散地震能量的作用。边坡上隔震支座的变形不相等将导致吊脚柱的变形不协调以及耗能和变形需求集中于边坡上方的支座，降低了系统的隔震能力，因此宜对边坡上布置不等侧向刚度的隔震支座，使得其侧向变形趋于一致。
3.4　吊脚柱剪力
人工波作用下各模型顺坡向中榀框架吊脚柱剪力值如图12所示。由图可知，基础隔震模型及层间隔震模型吊脚柱剪力之和均是小于无隔震模型，表明设置隔震支座可控制罕遇地震作用下结构吊脚层的剪力。此外，因吊脚层侧向刚度分布的不均匀性，无隔震模型与层间隔震模型吊脚柱剪力均有显著的不均匀性，剪力集中于吊脚短柱。由模型的柱剪力对比可知，设置基础隔震可减小吊脚柱剪力分配的不均匀程度。同时，大震下基础隔震模型吊脚短柱的剪力需求相较于无隔震模型以及层间隔震模型均有明显减轻，例如对于模型M1-2，其吊脚短柱的剪力仅为无隔震模型M1-1的21%、为层间隔震模型M1-3的38%。更小的剪力需求使得吊脚短柱在大震下损伤程度更低、安全裕度更大。相较于无隔震模型，设置层间隔震降低了吊脚层的内力响应，但因其未改变吊脚层刚度分布，其吊脚层剪力仍集中于吊脚短柱。对于模型M1-2，其吊脚短柱剪力最大值可达模型M1-1吊脚层剪力之和的47%，对于模型M1-2，其吊脚短柱剪力最大值可达模型M1-1吊脚层剪力之和的45%，均大于均匀分配下33%的比例，表明设置层间隔震吊脚短柱在大震下仍具有较高的剪力需求。
地震作用下吊脚柱内力分配的不均匀性导致吊脚层局部破坏较为严重，进而影响整体结构的安全性。在吊脚框架结构设计中，若采用增加吊脚短柱截面的方法，提高其安全储备，柱间刚度分布不均匀程度将随之增加，内力分布的不均匀性进一步加大[7]。因此为保障结构抗震安全，需对吊脚结构刚度分布的不均匀性加以控制。通过弹塑性分析结果可以发现，设置基础隔震可降低结构吊脚层剪力分布的不均匀性，为实现结构刚度控制提供新的技术途径。此外，虽然设置层间隔震吊脚短柱在大震下仍具有较高的剪力需求，但层间隔震降低了吊脚短柱的剪力需求，在结构设计中，与无隔震结构相比，吊脚短柱可按更小的截面尺寸进行设计，因此在一定程度上也可起到控制吊脚层刚度分布的不均匀程度的作用。
4　地震倒塌概率分析
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4.1　分析方法
为进一步研究2种隔震布置形式下结构的抗震性能，对模型M1-1、M1-2、M1-3开展增量动力时程分析（incremental dynamic analysis，IDA）[16]，对比模型的倒塌易损性，得到各模型在罕遇、极罕遇地震作用下的倒塌概率。
结构的地震倒塌易损性是指在不同强度地震动作用下，结构发生倒塌破坏状态概率。概率的计算公式为[17]
式中：FR为地震易损性；P为失效概率；EDP为结构地震需求参数；LS为结构的倒塌破坏状态；IM为地震动强度参数。并假定结构需求参数EDP与地震动强度参数IM服从指数分布[16]。
本文选取地震动峰值加速度PGA作为地震动强度参数IM。根据SHOME的研究成果[17]，选取10~20条地震波可基本满足结构抗震性能评估的需求。因此结合计算效率的考虑，本文在太平洋地震动中心的数据库PEER中选择了15条满足震中距和持时等要求的地震波开展易损性分析。15条地震动的加速度反应谱与中国规范反应谱的对比如图13所示。分别选取最大层间位移角θmax[18]、隔震支座的位移峰值Δmax作为评判混凝土框架部分及隔震装置破坏程度的地震需求参数EDP。根据规范及有关文献[19]，结构倒塌状态对应的θmax量化指标限值为1/50、Δmax限值为0.55倍隔震装置直径（0.55D）与3.0倍橡胶层总厚度（3.0Tr）的较小值。
4.2　分析结果
采用等间隔法，逐一对所选择强震地震动记录进行调幅，步长增量取0.15 g，第一次分析时PGA = 0.05 g。以条幅后的地震动为输入，对模型M1-1、M1-2、M1-3开展动力时程分析，按4.1节所述方法得到结构的倒塌易损性曲线，如图14所示。各模型在罕遇、极罕遇地震作用下的倒塌概率如表3所示。
由图14和表3可知，在地震作用下，层间隔震模型的倒塌概率明显小于无隔震模型，表明设置层间隔震可有效提高吊脚框架结构的抗地震倒塌能力。此外，在层间隔震模型中，由隔震装置失效所致结构倒塌的概率是大于混凝土框架部分的，表明层间隔震模型最终失效模式为隔震装置达到位移的极限状态，这与普通平地层间隔震结构的失效模式是一致的[20]。相对于设置层间隔震，设置基础隔震对提高吊脚框架结构抗地震倒塌性能的能力较弱。且在基础隔震模型中，由隔震装置失效所致倒塌的概率是小于混凝土框架部分的，表明结构最终失效模式为上部混凝土框架部分率先达到极限破坏状态。主要原因可能在于基础隔震模型中不同标高处的隔震支座未能协同工作，隔震装置未能充分发挥其减震效能。
5　结论
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针对吊脚结构不等高嵌固的特点，本文分别设计了无隔震、基础隔震、第二层柱底隔震（层间隔震）和3种吊脚框架结构算例。利用SAP2000有限元软件建立了结构算例的有限元分析模型，开展了弹性反应谱分析和弹塑性动力时程分析，考察隔震支座布置形式对吊脚框架结构地震响应、破坏模式以及地震倒塌概率等抗震性能的影响规律。得到以下主要结论：
1）设置基础隔震与层间隔震可控制结构的动力响应，其弹性分析的层剪力及弹塑性分析的损伤程度均明显小于无隔震模型的，从而可提高整体结构的安全裕度，为改善吊脚楼结构抗震性能提供了新的途径。
2）设置基础隔震可改善结构刚度分布的不均匀性，显著减小吊脚柱之间内力分布的差异，避免剪力集中于吊脚短柱，提高结构安全储备。沿边坡布置的隔震支座变形具有不一致性，其将导致耗能和变形需求集中于边坡上方的支座，降低了系统的隔震能力，导致其不能有效提高结构抗地震倒塌能力。因此在基础隔震模型中宜沿边坡采用不同侧向刚度的隔震支座，减小隔震支座的变形差异。
3）与基础隔震相比，设置层间隔震对结构损伤控制的能力更优，且结构上部层间位移角随楼层的分布更为均匀，可有效避免侧向位移集中于局部楼层，降低结构的倒塌概率。虽然设置层间隔震吊脚短柱在大震下仍具有较高的剪力需求，但其降低了吊脚短柱的剪力需求，在结构设计中，与无隔震结构相比，吊脚短柱可按更小的截面尺寸进行设计，因此在一定程度上也可起到控制吊脚层刚度分布的不均匀程度的作用。
基金
收起
  • 国家自然科学基金项目(51878101; 52278481)
  • 重庆市建设科技项目(城科字2020第3-16)
  • 重庆市研究生科研创新项目(CYB22030)
文献
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2024年第44卷第1期
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文章信息
doi: 10.13197/j.eeed.2024.0114
  • 接收时间：2022-10-07
  • 首发时间：2026-03-30
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  • 收稿日期：2022-10-07
  • 修回日期：2023-03-20
基金
国家自然科学基金项目(51878101; 52278481)
重庆市建设科技项目(城科字2020第3-16)
重庆市研究生科研创新项目(CYB22030)
作者信息
    1.重庆大学 土木工程学院，重庆 400045
    2.重庆大学 工程结构抗震防灾重庆市重点实验室，重庆 400045

通讯作者:

刘立平（1971—），男，教授，博士，主要从事结构抗震分析及设计理论研究。E-mail：
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2种不同金属材料的力学参数
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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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