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Article(id=1241791798817915266, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241791788986471392, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2025.0316, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1715184000000, receivedDateStr=2024-05-09, revisedDate=1729094400000, revisedDateStr=2024-10-17, acceptedDate=null, acceptedDateStr=null, onlineDate=1773995836213, onlineDateStr=2026-03-20, pubDate=1751212800000, pubDateStr=2025-06-30, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773995836213, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773995836213, creator=13701087609, updateTime=1773995836213, updator=13701087609, issue=Issue{id=1241791788986471392, tenantId=1146029695717560320, journalId=1241701559352995854, year='2025', volume='45', issue='3', pageStart='1', pageEnd='231', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773995833869, creator=13701087609, updateTime=1773996997624, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241796670220993006, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241791788986471392, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241796670220993007, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241791788986471392, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=180, endPage=190, ext={EN=ArticleExt(id=1241791800055234976, articleId=1241791798817915266, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Seismic response analysis of Fe-SMA-double variable friction pendulum bearing isolated continuous beam bridge under near-fault ground motions, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

To address issues such as excessive displacement and inadequate self-resetting capabilities in isolated bridges employing traditional double concave friction pendulum bearings, a novel iron-based shape memory alloy-double variable friction pendulum bearing (Fe-SMA-DVFPB) was developed. This bearing integrates the variable friction mechanism on the sliding surface with the superelastic properties of shape memory alloy. A constitutive model for the bearing is established, and its equivalent analysis model is determined through theoretical analysis and numerical simulation. Based on practical engineering considerations, isolated bridges with different types of bearings are designed, and their seismic performance under near-fault ground motions is analyzed. The results show that the maximum isolator displacements of the three types of isolation structures under pulse-type earthquakes are 2.1, 1.63 and 1.47 times greater than those under non-pulse-type earthquakes, respectively. Compared to DCFPB-isolated bridges, Fe-SMA-DVFPB-isolated bridges exhibit the maximum reduction in isolator displacement of 38.9% under pulse-type earthquakes and 13% under non-pulse-type earthquakes. Additionally, the maximum reduction in residual displacement is 93.5% for pulse-type and 83.1% for non-pulse-type earthquakes. The use of Fe-SMA-DVFPB significantly improves control over both relative displacement and residual displacement. The reduction in relative displacement and residual displacement in Fe-SMA-DVFPB-isolated bridge bearings is significantly greater than the increase in bending moment and shear force at the pier base. Fe-SMA-DVFPB can further enhance the post-earthquake resilience of bridges.

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针对传统摩擦复摆支座（double concave friction pendulum bearing，DCFPB）隔震桥梁在近断层地震中支座位移过大、自复位能力不足等问题，利用滑移面变摩擦方式和形状记忆合金的超弹性特性，研发了一种铁基形状记忆合金变摩擦复摆隔震支座（iron-based shape memory alloy-double variable friction pendulum bearing，Fe-SMA-DVFPB）。利用理论分析和数值模拟的方法，构建了新型支座本构模型，确定了其等效分析模型。以实际工程为背景，分别设计了应用不同类型支座的隔震桥梁，并研究了其在近断层地震动作用下的抗震性能。研究表明：3种隔震结构在脉冲型地震作用下支座最大位移分别为非脉冲型地震作用下的2.1、1.63、1.47倍；相比DCFPB隔震桥梁，Fe-SMA-DVFPB隔震桥梁支座位移最大减小量为38.9%（脉冲型）和13%（非脉冲型），残余位移最大减小量为93.5%（脉冲型）和83.1%（非脉冲型）；应用Fe-SMA-DVFPB能更有效地控制支座位移与残余位移；Fe-SMA-DVFPB隔震桥梁支座位移与残余位移减小量明显大于墩底弯矩与墩底剪力增加量。Fe-SMA-DVFPB能够进一步提升桥梁的震后可恢复能力。

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韩建平（1970—），男，教授，博士，主要从事结构抗震与减震控制、结构健康监测与损伤诊断研究。E-mail：
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尚继英（1987—），男，讲师，博士，主要从事结构隔震控制研究。E-mail：

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尚继英（1987—），男，讲师，博士，主要从事结构隔震控制研究。E-mail：

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尚继英（1987—），男，讲师，博士，主要从事结构隔震控制研究。E-mail：

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journalId=1241701559352995854, articleId=1241791798817915266, language=CN, label=图15, caption=两类地震动下支座残余位移对比, figureFileSmall=K5sW30Bv0DVNMvhPJqwkKw==, figureFileBig=lMV6Z+X+O7Bj8XC0PEPd5A==, tableContent=null), ArticleFig(id=1241802914323300874, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=EN, label=Fig. 16, caption=Comparison of pier base bending moments in different bridge structures under near-fault ground motions, figureFileSmall=aNh0aZ9RHxyTaUIp73PPvw==, figureFileBig=5/nTy2T3OHXfiDnw5dwiQg==, tableContent=null), ArticleFig(id=1241802914428158489, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=CN, label=图16, caption=近断层地震下不同桥梁墩底弯矩对比, figureFileSmall=aNh0aZ9RHxyTaUIp73PPvw==, figureFileBig=5/nTy2T3OHXfiDnw5dwiQg==, tableContent=null), ArticleFig(id=1241802914549793321, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=EN, label=Fig. 17, caption=Comparison of pier base shear forces in different bridges under near-fault ground motions, figureFileSmall=ZRsrzYvGxQoyCQe6KPQnqQ==, figureFileBig=eXAGWDZ/5GTcNrXaNf47jA==, tableContent=null), ArticleFig(id=1241802914671428151, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=CN, label=图17, caption=近断层地震下不同桥梁墩底剪力对比, figureFileSmall=ZRsrzYvGxQoyCQe6KPQnqQ==, figureFileBig=eXAGWDZ/5GTcNrXaNf47jA==, tableContent=null), ArticleFig(id=1241802914851783246, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=EN, label=Table 1, caption=

Parameters of DVFPB

, figureFileSmall=null, figureFileBig=null, tableContent=
R/mmμ1μ2μ3r1/mm
20000.030.050.07120
), ArticleFig(id=1241802914969223769, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=CN, label=表1, caption=

DVFPB参数取值

, figureFileSmall=null, figureFileBig=null, tableContent=
R/mmμ1μ2μ3r1/mm
20000.030.050.07120
), ArticleFig(id=1241802915065692772, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=EN, label=Table 2, caption=

Comparison of periods of non-isolated bridges and isolated bridges

, figureFileSmall=null, figureFileBig=null, tableContent=
结构类型非隔震DCFPBDVFPBFe-SMA-DVFPB
Tiso0.973.172.652.36
), ArticleFig(id=1241802915166356078, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=CN, label=表2, caption=

非隔震桥梁和隔震桥梁周期对比

, figureFileSmall=null, figureFileBig=null, tableContent=
结构类型非隔震DCFPBDVFPBFe-SMA-DVFPB
Tiso0.973.172.652.36
), ArticleFig(id=1241802915300573823, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=EN, label=Table 3, caption=

Parameters of the selected ground motion records

, figureFileSmall=null, figureFileBig=null, tableContent=
非脉冲型脉冲型
地震动编号台站Rjb/kmPGA/gPGV/（cm/s）地震动编号台站Rjb/kmPGA/gPGV/（cm/s）
1CHY074-E10.80.2331.41TCU104-N12.90.0947.5
2TCU089-N9.00.2333.12TCU036-N19.80.1347.5
3CHY029-N11.00.2439.73TCU103-E6.00.1370.2
4CHY029-E11.00.2935.24TCU036-E19.80.1457.5
5CHY041-E19.80.320.45TCU039-N19.90.1456.3
6TCU076-E2.70.3451.86TCU109-E13.00.1556.9
7TCU089-E9.00.3535.07TCU109-N13.00.1656.4
8TCU072-N7.10.3852.58TCU102-N1.50.1766.4
9TCU074-N13.80.3844.99TCU128-N13.10.1762.6
10TCU076-N2.70.4359.710TCU039-E19.90.2055.3
11TCU084-N11.40.4348.111TCU120-E7.40.2359.8
12TCU078-E8.20.4540.212TCU102-E1.50.3091.7
), ArticleFig(id=1241802915489317516, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=CN, label=表3, caption=

地震动记录参数

, figureFileSmall=null, figureFileBig=null, tableContent=
非脉冲型脉冲型
地震动编号台站Rjb/kmPGA/gPGV/（cm/s）地震动编号台站Rjb/kmPGA/gPGV/（cm/s）
1CHY074-E10.80.2331.41TCU104-N12.90.0947.5
2TCU089-N9.00.2333.12TCU036-N19.80.1347.5
3CHY029-N11.00.2439.73TCU103-E6.00.1370.2
4CHY029-E11.00.2935.24TCU036-E19.80.1457.5
5CHY041-E19.80.320.45TCU039-N19.90.1456.3
6TCU076-E2.70.3451.86TCU109-E13.00.1556.9
7TCU089-E9.00.3535.07TCU109-N13.00.1656.4
8TCU072-N7.10.3852.58TCU102-N1.50.1766.4
9TCU074-N13.80.3844.99TCU128-N13.10.1762.6
10TCU076-N2.70.4359.710TCU039-E19.90.2055.3
11TCU084-N11.40.4348.111TCU120-E7.40.2359.8
12TCU078-E8.20.4540.212TCU102-E1.50.3091.7
), ArticleFig(id=1241802915636118171, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=EN, label=Table 4, caption=

Average displacement of the maximum displacement of three types of bearings

, figureFileSmall=null, figureFileBig=null, tableContent=
地震类型支座类型最大支座位移/mm最大位移变化量/%
脉冲型DCFPB286.9—
DVFPB200.9-30.0
Fe-SMA-DVFPB175.3-38.9
非脉冲型DCFPB136.8—
DVFPB123.3-9.9
Fe-SMA-DVFPB119.0-13.0
), ArticleFig(id=1241802917200593573, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=CN, label=表4, caption=

3种支座最大位移的位移平均值

, figureFileSmall=null, figureFileBig=null, tableContent=
地震类型支座类型最大支座位移/mm最大位移变化量/%
脉冲型DCFPB286.9—
DVFPB200.9-30.0
Fe-SMA-DVFPB175.3-38.9
非脉冲型DCFPB136.8—
DVFPB123.3-9.9
Fe-SMA-DVFPB119.0-13.0
), ArticleFig(id=1241802917368365747, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=EN, label=Table 5, caption=

Average value of residual displacement of three types of bearings

, figureFileSmall=null, figureFileBig=null, tableContent=
地震类型支座类型支座残余位移/mm残余位移变化量/%
脉冲型DCFPB8.65—
DVFPB9.05+4.6
Fe-SMA-DVFPB0.56-93.5
非脉冲型DCFPB4.55—
DVFPB4.92+8.1
Fe-SMA-DVFPB0.77-83.1
), ArticleFig(id=1241802917481611971, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=CN, label=表5, caption=

3种支座残余位移平均值

, figureFileSmall=null, figureFileBig=null, tableContent=
地震类型支座类型支座残余位移/mm残余位移变化量/%
脉冲型DCFPB8.65—
DVFPB9.05+4.6
Fe-SMA-DVFPB0.56-93.5
非脉冲型DCFPB4.55—
DVFPB4.92+8.1
Fe-SMA-DVFPB0.77-83.1
), ArticleFig(id=1241802917628412627, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=EN, label=Table 6, caption=

Average values of pier base bending moments and shear forces for three types of bearing-isolated bridges

, figureFileSmall=null, figureFileBig=null, tableContent=
地震类型支座类型墩底弯矩/（×103 kN•m）墩底弯矩变化量/%墩底剪力/（×103 kN）墩底剪力变化量/%
脉冲型非隔震16.63—2.54—
DCFPB7.55—0.65—
DVFPB7.86+4.10.62-4.6
Fe-SMA-DVFPB7.80+3.30.67+3.1
非脉冲型非隔震14.77—2.56—
DCFPB7.63—0.65—
DVFPB7.65+0.30.650
Fe-SMA-DVFPB8.41+10.20.63-3.1
), ArticleFig(id=1241802917771018984, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791798817915266, language=CN, label=表6, caption=

3种支座隔震桥梁墩底弯矩和墩底剪力平均值

, figureFileSmall=null, figureFileBig=null, tableContent=
地震类型支座类型墩底弯矩/（×103 kN•m）墩底弯矩变化量/%墩底剪力/（×103 kN）墩底剪力变化量/%
脉冲型非隔震16.63—2.54—
DCFPB7.55—0.65—
DVFPB7.86+4.10.62-4.6
Fe-SMA-DVFPB7.80+3.30.67+3.1
非脉冲型非隔震14.77—2.56—
DCFPB7.63—0.65—
DVFPB7.65+0.30.650
Fe-SMA-DVFPB8.41+10.20.63-3.1
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Fe-SMA-变摩擦复摆隔震连续梁桥近断层下地震反应研究
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尚继英 1, 2 , 娄东旭 1 , 韩建平 1 , 郁银泉 2 , 宋炳磊 1
地震工程与工程振动 | 2025,45(3): 180-190
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地震工程与工程振动 | 2025, 45(3): 180-190
Fe-SMA-变摩擦复摆隔震连续梁桥近断层下地震反应研究
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尚继英1, 2 , 娄东旭1, 韩建平1 , 郁银泉2, 宋炳磊1
作者信息
  • 1.兰州理工大学 土木工程学院，甘肃 兰州 730050
  • 2.中国建筑标准设计研究院有限公司，北京 100048

    • 尚继英（1987—），男，讲师，博士，主要从事结构隔震控制研究。E-mail：

通讯作者:

韩建平（1970—），男，教授，博士，主要从事结构抗震与减震控制、结构健康监测与损伤诊断研究。E-mail：
Seismic response analysis of Fe-SMA-double variable friction pendulum bearing isolated continuous beam bridge under near-fault ground motions
Jiying SHANG1, 2 , Dongxu LOU1, Jianping HAN1 , Yinquan YU2, Binglei SONG1
Affiliations
  • 1.School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China
  • 2.China Institute of Building Standard Design and Research Co., Ltd., Beijing 100048, China
出版时间: 2025-06-30 doi: 10.13197/j.eeed.2025.0316
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摘要
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针对传统摩擦复摆支座（double concave friction pendulum bearing，DCFPB）隔震桥梁在近断层地震中支座位移过大、自复位能力不足等问题，利用滑移面变摩擦方式和形状记忆合金的超弹性特性，研发了一种铁基形状记忆合金变摩擦复摆隔震支座（iron-based shape memory alloy-double variable friction pendulum bearing，Fe-SMA-DVFPB）。利用理论分析和数值模拟的方法，构建了新型支座本构模型，确定了其等效分析模型。以实际工程为背景，分别设计了应用不同类型支座的隔震桥梁，并研究了其在近断层地震动作用下的抗震性能。研究表明：3种隔震结构在脉冲型地震作用下支座最大位移分别为非脉冲型地震作用下的2.1、1.63、1.47倍；相比DCFPB隔震桥梁，Fe-SMA-DVFPB隔震桥梁支座位移最大减小量为38.9%（脉冲型）和13%（非脉冲型），残余位移最大减小量为93.5%（脉冲型）和83.1%（非脉冲型）；应用Fe-SMA-DVFPB能更有效地控制支座位移与残余位移；Fe-SMA-DVFPB隔震桥梁支座位移与残余位移减小量明显大于墩底弯矩与墩底剪力增加量。Fe-SMA-DVFPB能够进一步提升桥梁的震后可恢复能力。

铁基形状记忆合金  /  变摩擦复摆隔震支座  /  本构模型  /  分析模型  /  近断层地震作用  /  抗震性能

To address issues such as excessive displacement and inadequate self-resetting capabilities in isolated bridges employing traditional double concave friction pendulum bearings, a novel iron-based shape memory alloy-double variable friction pendulum bearing (Fe-SMA-DVFPB) was developed. This bearing integrates the variable friction mechanism on the sliding surface with the superelastic properties of shape memory alloy. A constitutive model for the bearing is established, and its equivalent analysis model is determined through theoretical analysis and numerical simulation. Based on practical engineering considerations, isolated bridges with different types of bearings are designed, and their seismic performance under near-fault ground motions is analyzed. The results show that the maximum isolator displacements of the three types of isolation structures under pulse-type earthquakes are 2.1, 1.63 and 1.47 times greater than those under non-pulse-type earthquakes, respectively. Compared to DCFPB-isolated bridges, Fe-SMA-DVFPB-isolated bridges exhibit the maximum reduction in isolator displacement of 38.9% under pulse-type earthquakes and 13% under non-pulse-type earthquakes. Additionally, the maximum reduction in residual displacement is 93.5% for pulse-type and 83.1% for non-pulse-type earthquakes. The use of Fe-SMA-DVFPB significantly improves control over both relative displacement and residual displacement. The reduction in relative displacement and residual displacement in Fe-SMA-DVFPB-isolated bridge bearings is significantly greater than the increase in bending moment and shear force at the pier base. Fe-SMA-DVFPB can further enhance the post-earthquake resilience of bridges.

iron-based shape memory alloy  /  double variable friction pendulum bearing  /  constitutive model  /  analysis model  /  near-fault ground motions  /  seismic performance
尚继英, 娄东旭, 韩建平, 郁银泉, 宋炳磊. Fe-SMA-变摩擦复摆隔震连续梁桥近断层下地震反应研究. 地震工程与工程振动, 2025 , 45 (3) : 180 -190 . DOI: 10.13197/j.eeed.2025.0316
Jiying SHANG, Dongxu LOU, Jianping HAN, Yinquan YU, Binglei SONG. Seismic response analysis of Fe-SMA-double variable friction pendulum bearing isolated continuous beam bridge under near-fault ground motions[J]. Earthquake Engineering and Engineering Dynamics, 2025 , 45 (3) : 180 -190 . DOI: 10.13197/j.eeed.2025.0316
正文
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0　引言
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近场地震动相比远场地震动，具有高能量、长周期及脉冲幅值大的特点[1-2]，近场地震动又称近断层地震动，通常可分为脉冲型地震动和非脉冲型地震动。地震发生时，大部分能量会在极短的时间内输入到桥梁结构中，对于桥梁结构造成更为严重的破坏。
摩擦摆隔震支座（friction pendulum bearing，FPB）由于具有稳定的力学性能、较大的竖向承载力等优点，在桥梁结构的减隔震设计中得到广泛应用。传统FPB滑移面的摩擦系数和曲率半径固定不变，这会导致在长周期脉冲地震作用下产生过大位移的问题。为此，TSAI等[3-4]提出了双曲面摩擦摆隔震支座（double concave friction pendulum bearing，DCFPB），DCFPB有2个滑移面，其变形是由滑块在这2个滑移面上同时滑动引起，使得支座的变形能力增大。SHANG等[5]提出了一种变摩擦摆隔震支座（variable friction pendulum bearing，VFPB）。VFPB结合了变摩擦机制，将滑移面打磨成不同粗糙程度的滑移区，在不影响支座隔震效果的同时，达到支座限位的目的，使支座自适应特性更为明确，然而，VFPB在大震作用下限制位移效果不佳，残余位移过大，且支座边缘滑移区摩擦系数增大，会导致支座的自复位特性降低。
形状记忆合金（shape memory alloy，SMA）具有独特的超弹性特性和形状记忆效应，可有效提升支座恢复能力[6-7]，20世纪90年代以来，众多学者提出了多种含有SMA丝的阻尼器和隔震器[8-10]。ZHENG等[11]提出SMA-FPB复合型隔震支座，研究表明：基于SMA的FPB不仅可以有效地改善传统FPB能量耗散的问题，还可以增强桥梁的抗震性能，尤其是在残余位移控制方面。王萌等[12]结合SMA与负刚度（negative stiffness device，NSD）隔震支座各自的优点，提出一种间隙式SMA-NSD摩擦隔震支座并进行隔震性能研究。结果表明，该支座可显著降低NSD支座引起的残余变形并同时有效控制SMA支座引起的内力响应。李忠献等[13]提出了一种基于SMA的复合橡胶支座并在多跨简支桥中加以应用，其研究结果表明，相比于普通橡胶支座，SMA复合橡胶支座具有良好的隔震与自复位效果。DEZFULI等[14]对SMA-天然橡胶隔震支座进行了力学性能研究，结果显示其性能稳定并具有良好的滞回耗能能力。SMA应用到隔震支座中可以显著减少支座残余位移，提高支座的自复位能力。
铁基形状记忆合金（iron-based shape memory alloy，Fe-SMA）在强度、塑性和成形加工等方面性能优越，且其生产成本远低于其他类型SMA，因而更适合在土木工程结构领域中的应用[15]。为此，本研究将DCFPB与滑移面变摩擦方式和Fe-SMA相结合，提出一种兼具自复位和自适应特性的变摩擦复摆隔震支座—铁基形状记忆合金变摩擦复摆隔震支座（iron-based shape memory alloy-double variable friction pendulum bearing，Fe-SMA-DVFPB），研究其运行原理和力学行为，构建其本构模型，提出新型支座等效分析模型，验证了等效分析模型的正确性。并在此基础上对Fe-SMA-DVFPB隔震连续梁桥在近断层地震动作用下进行地震反应研究，研究在近断层地震下的隔震桥梁的减震机理及抗震性能。
1　基本构造
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DVFPB由上、下连接座板以及位于两者中间的上、下铰接滑块组构成，下座板上表面与上座板下表面的球形凹面划分成具有不同粗糙度的滑移区域，见图1（a）。Fe-SMA-DVFPB由DVFPB与Fe-SMA拉索组合构造而成，Fe-SMA拉索由多个Fe-SMA丝线绞制而成，Fe-SMA索位于支座外侧斜拉交叉成X型，通过端部锚固装置与支座座板相连，滑块组可分别在上、下连接座板的曲面内滑动，见图1（b）。滑块组由上、下滑块通过球铰连接组成。上滑块上表面及下滑块下表面覆盖滑移材料，上、下滑移面摩擦系数由中心向边缘逐渐增大。
2　本构模型构建
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Fe-SMA-DVFPB作为一种复合支座，其恢复力模型为Fe-SMA单元与DVFPB单元的叠加，故其理论本构只需将2种单元对应本构分别推导后叠加即可。
2.1　DVFPB本构模型
对于上、下滑移面对称的DVFPB，其本构模型与VFPB相同。基于SHANG等[16]对于VFPB本构模型的研究，DVFPB本构如式（1）所示：
式中：W为上部结构施加到支座上的竖向力；x为滑块在滑移面上的相对位移；Re = 2R，R为上、下座板球形凹面的曲率半径；F为下连接座板受到的水平力；fmin为滑移面最小摩擦力；t为最小摩擦力fmin到最大摩擦力fmax的增加率。CALVI等[17]研究表明，当滑移面上滑移区分布均匀，且滑块直径为滑移区宽度的1~2倍时，由变摩擦机制引起的摩擦力从中心滑移区到边缘滑移区线性增加。
2.2　Fe-SMA本构模型
本研究只利用Fe-SMA中的超弹性效应，考虑到实用性和简便性，采用Auricchio本构模型[18]。Fe-SMA-DVFPB支座的计算简图见图2。图中实线部分表示支座初始图，虚线部分表示支座变形图，运动中假设下座板不移动，θ为下滑块相对于滑动面中心的旋转角；β0为拉索初始状态下与底板的夹角；x、y分别为滑块上O点到O′点的水平和竖向距离；x′和y′分别为上座板上A点到A′的水平和竖向距离，其中x = x′，y = y′；L0为拉索初始长度，L为拉索变形后的长度。支座滑移面上不同滑移区的划分示意图见图3。图中从中心到边缘滑移区粗糙度依次增加，区域C1、C2、C3外缘对应圆的半径分别为r1、r2、r3，C1区域对应的摩擦系数为μ1，C2区域对应的摩擦系数为μ2，C3区域对应的摩擦系数为μ3，且满足μ1<μ2<μ3，阴影面积表示滑块与滑移面的接触部分，滑块与滑移面接触区域为C0，半径为r0。
选x为基本变量，可知：
而θ足够小，θ≈tanθ≈sinθ = x/2R。竖向位移和水平位移的关系为
由图2支座变形后受力图可知，变形后Fe-SMA的伸长量为
由式（3）和式（4）可求得Fe-SMA拉索的伸长量与支座水平位移的关系为
因此，Fe-SMA的应变为
为简化Fe-SMA本构，将唯象理论本构模型中的Auricchio进行理想化[18]，其简化后的Fe-SMA本构模型见图4。
设OA段斜率为k1，AB段斜率为k2，、、、分别为马氏体阶段开始和结束的应力和应变，、、、分别为奥氏体阶段开始和结束的应力和应变，则简化后旗帜形的Fe-SMA本构关系如式（7）所示：
因此，Fe-SMA提供的水平恢复力为
式中：m为拉索的股数；A为每股拉索截面面积；σ（ε）为拉索应力；先根据式（6）求得ε，再由Fe-SMA的本构关系求得σ。
可进一步求得Fe-SMA拉索在水平方向的恢复力为
式中：β为拉索变形后与底板的夹角，有
2.3　Fe-SMA-DVFPB本构模型
Fe-SMA-DVFPB支座水平方向恢复力为相同位移的Fe-SMA和DVFPB恢复力的和，即
将式（1）与式（9）代入式（11）中可得：
3　等效分析模型
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新型Fe-SMA-DVFPB表现出的滞回规则不同于目前常用隔震支座的滞回规则，本文通过组合现有支座单元模拟Fe-SMA-DVFPB的非线性特性。
3.1　等效分析模型原理
本文提出一种并联模型模拟Fe-SMA-DVFPB的非线性特性，该并联模型由多个已有的非线性连接单元并联而成。基于有限元分析软件SAP2000，并联friction pendulum isolation（FPI）单元和damper-friction spring（D-FS）单元模拟DVFPB；并联multilinear elastic（ML-E）单元与multilinear plastic（ML-P）单元模拟Fe-SMA。
3.2　并联模型
DVFPB的滞回曲线见图5（a），可以等价为一个FPI单元和D-FS单元的组合，分别见图5（b）、（c），D-FS用于表达与位移相关的摩擦阻尼特性。Fe-SMA的滞回曲线见图6（a），可以等价为一个ML-P单元和ML-E单元的组合，分别见图6（b）、（c）。Fe-SMA-DVFPB的滞回曲线见图7（a），可以等价为一个DVFPB模型和Fe-SMA模型的组合，分别见图7（b）、（c）。
3.3　等效分析模型验证
并联模型在结构分析软件中容易实现，仅需要在2个节点之间将多个不同的连接单元重叠连接。并联模型表现出的特性是这些单元特性的简单叠加。通过合理的参数修正，并联模型能够精确地模拟Fe-SMA-DVFPB的真实滞回特性。本文通过分析模型和理论分析结果的对比来验证等效分析模型的正确性。
分析模型在有限元软件中的实施方式见图8，4个单元重叠连接于节点A和B之间，4个单元共享2个节点。上节点A与上部结构连接，下节点B刚接到下部结构或地面。4个单元指定相同的竖向刚度，共同分担作用于支座的竖向荷载。
为了验证本文所提出的等效分析模型的正确性，取如下参数的支座作为验证算例。DVFPB参数：R = 2 m，r0 = 120 mm，r1 = 200 mm，r2 = 300 mm，r3 = 400 mm，μ1 = 0.03，μ2 = 0.05，μ3 = 0.07，W = 600 kN，x = 230 mm。Fe-SMA参数：k1 = 443 kN/mm，k2 = 38kN/mm，，，，。理论分析和有限元模型所得支座滞回曲线见图9。由图可知，2种方法所得滞回曲线能较好的吻合，滞回曲线所围面积相对差在5%以内，且支座最大位移处的等效刚度相对差为9.03%。由此可以得出，所提出的等效分析模型能够正确地反映新型支座的滞回特性。
4　工程实例
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4.1　工程概况
拟建K18+040飞龙大桥位于广西壮族自治区南宁市横县平马镇与新福镇飞龙乡交界处，由北至南跨越郁江，全桥总长940 m。其中引桥长360 m，引桥桥跨布置：平马侧为（5×30）m先简支后连续预应力混凝土T梁，沙坪侧为（7×30）m先简支后连续预应力混凝土T梁。桥面全宽13 m，横向共布置6片T梁。单个桥墩的基础平面图见图10。
根据GB 18306—2015《中国地震动参数区划图》[19]规定，桥址区域地震动峰值加速度为0.1 g，对应的地震基本烈度为Ⅶ度。根据现场地勘显示，桥址处场地类别为Ⅱ类，地震动反应谱特征周期为0.35 s。
4.2　有限元模拟
根据飞龙大桥引桥的设计方案，建立三维有限元动力计算模型进行抗震性能分析，计算模型以顺桥向为X轴，横桥向为Y轴，竖桥向为Z轴。采用非线性时程法分析时，主梁和桥墩均采用空间梁单元模拟。飞龙大桥引桥动力计算有限元模型见图11。
4.3　支座设计
首先确定隔震桥梁周期Tiso。本文取Tiso = 2T0，其中T0为非隔震桥梁的基本周期。基于隔震周期Tiso，通过迭代[20]确定隔震支座在设防烈度下的位移为35 mm。DVFPB设计参数见表1。
为形成与DVFPB和Fe-SMA-DVFPB隔震结构工程需求参数的对比，DCFPB的曲率半径与DVFPB相同，DCFPB滑移面上的摩擦系数取值与DVFPB中心区域的摩擦系数μ1相同，Fe-SMA单元参数确定为k1 = 443 kN/mm，k2 = 38 kN/mm，，，，，Fe-SMA拉索由0.8 mm单丝直径×7丝×7股绞合构成，通过ASGARIAN等[21]的研究表明，SMA可以在应变8%~10%范围内表现出较好的自复位能力，但是在大应变循环荷载下退化较明显，因此建议设计最大应变值宜控制在6%。支座布置时，由于桥墩分布较规则，采用“一墩一支座”的原则，一共选用16个支座，在桥墩墩顶布置支座，上座板与梁底面相连，下座板与桥墩垫石相连。DCFPB、DVFPB和Fe-SMA-DVFPB隔震桥梁以及非隔震桥梁的周期见表2。
4.4　地震动输入
根据工程场地地震动参数和场地条件，结合JTG/T B02-01—2008《公路桥梁抗震设计细则》[22]，从美国太平洋地震工程研究中心（Pacific Earthquake Engineering Research Center，PEER）数据库中选取24条典型近断层地震动记录，其中近断层脉冲型（PGV/PGA>0.2）和非脉冲型（PGV/PGA<0.2）地震动记录各12条，近断层地震动记录见表3。选取原则是：①为排除震源特性对地震动的影响，采取相同地震事件的地震动记录，本文均从集集地震（Chi-Chi）选取；②断层距在20 km以内；③震级不小于5.5级；④地震动峰值加速度大于0.1 g。
4.5　结果分析
4.5.1　支座位移
在12条非脉冲型与12条脉冲型地震动作用下，对于分别采用DCFPB、DVFPB和Fe-SMA-DVFPB隔震支座的桥梁结构体系进行时程分析。
Fe-SMA-DVFPB隔震桥梁同一支座在脉冲型地震动（TCU036-E）和非脉冲型地震动（CHY029-E）下滞回曲线对比见图12。可以看出脉冲型地震动具有比非脉冲型地震动更大的能量，对支座造成更大的位移。Fe-SMA-DVFPB最大位移为108 mm，此时Fe-SMA拉索满足极限位移要求。
结构在CHY029-E（非脉冲型）和TCU036-E（脉冲型）地震动作用下3种类型隔震支座位移时程分析对比见图13。可以看出，脉冲型地震动会比非脉冲型地震动对桥梁结构造成更大的位移，并且在脉冲型地震动作用下，位移时程最大峰值为第二大峰值的2倍以上，有一个明显的“突起”。
桥梁结构在2种类型地震动作用下所得支座最大位移对比见图14。图中将2种类型地震动产生的支座位移绘制于同一坐标系下，当表示位移的散点图位于对角线上方时表示纵轴代表的支座位移大于横轴代表的支座位移，反之则表示横轴代表的支座位移大于纵轴代表的支座位移。可以看出，在2种类型地震动下，散点均在对角线以上，即在脉冲型地震动作用下支座位移均大于非脉冲型地震动作用下支座位移。DCFPB、DVFPB与Fe-SMA-DVFPB在两类地震动作用下最大支座位移的平均值见表4。其中DCFPB在脉冲型地震动作用下位移为非脉冲型的2.1倍；DVFPB在脉冲型地震动作用下位移为非脉冲型的1.63倍；Fe-SMA-DVFPB在脉冲型地震动作用下位移为非脉冲型的1.47倍。显然，脉冲型地震动会对3种支座的隔震桥梁造成更大的支座位移响应，下面将对DCFPB、DVFPB与Fe-SMA-DVFPB在脉冲型地震动与非脉冲型地震动下的减震效果进行详细的研究。
由表4可知，相比DCFPB，DVFPB和Fe-SMA-DVFPB能更好地控制支座位移。而Fe-SMA-DVFPB中Fe-SMA索对支座提供了一定的拉力使支座位移进一步的减小，这表明采用变摩擦方式和Fe-SMA拉索可以进一步控制DCFPB隔震结构在近断层地震作用下的支座位移。
4.5.2　支座残余位移
隔震桥梁在2种类型地震动作用下支座残余位移对比见图15。由图可知，对于DCFPB与DVFPB，散点均在对角线以上，即在脉冲型地震动作用下支座残余位移均大于非脉冲型地震动作用下的支座残余位移。DCFPB、DVFPB与Fe-SMA-DVFPB在两类型地震动作用下支座残余位移的平均值见表5。其中DCFPB在脉冲型地震动作用下残余位移平均值为非脉冲型的1.9倍；DVFPB在脉冲型地震动作用下残余位移平均值为非脉冲型的1.84倍。而对于Fe-SMA-DVFPB，不论在脉冲型地震动还是非脉冲型地震动作用下，支座残余位移均得到有效控制，残余位移最大值仅为2.76 mm，远小于DCFPB和DVFPB的残余位移，这是由于Fe-SMA-DVFPB利用了Fe-SMA索的超弹性特性从而大幅减小支座的残余位移。
由表5可知，相比于DCFPB与DVFPB，Fe-SMA-DVFPB隔震桥梁支座的残余位移大幅减小。这表明采用Fe-SMA拉索可以进一步提升DVFPB隔震结构在近断层地震作用下的减震性能。
4.5.3　墩底弯矩与墩底剪力响应
非隔震桥梁与3种隔震桥梁在近断层地震作用下墩底弯矩的对比见图16。由图可知，不论在脉冲型还是非脉冲型地震作用下，隔震支座均能有效减小墩底弯矩，并且3种隔震桥梁的墩底弯矩相差不大。
非隔震桥梁与3种隔震桥梁在近断层地震作用下墩底剪力的对比见图17。由图可知，不论在脉冲型还是非脉冲型地震作用下，隔震支座均能有效减小墩底剪力，并且3种隔震桥梁的墩底剪力相差不大。
非隔震结构、DCFPB、DVFPB与Fe-SMA-DVFPB结构在12条脉冲型地震动与12条非脉冲型地震动下桥梁结构的墩底剪力与墩底弯矩平均值见表6。由表可知，3种隔震桥梁的墩底弯矩值与墩底剪力值相差不大，均小于非隔震桥梁的墩底弯矩，说明在近断层地震作用下，3种支座对于隔震桥梁的墩底弯矩与墩底剪力均能得到有效控制，并且控制效果相当。因此，Fe-SMA-DVFPB结构在控制支座位移与残余位移的同时，不会明显增大其墩底弯矩与剪力。
5　结论
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1）研发了一种新型的Fe-SMA-DVFPB隔震支座，研究其力学行为，构建其本构模型，提出了该支座的等效分析模型并验证了该模型的正确性。
2）相比于DCFPB支座，DVFPB支座位移最大减小量为30%（脉冲型）和9.9%（非脉冲型），残余位移增加，且最大增加量为4.6%（脉冲型）和8.1%（非脉冲型）；Fe-SMA-DVFPB支座位移最大减小量为38.9%（脉冲型）和13%（非脉冲型），残余位移最大减小量为93.5%（脉冲型）和83.1%（非脉冲型）。Fe-SMA-DVFPB支座能更有效地控制支座相对位移与残余位移，并且Fe-SMA-DVFPB隔震桥梁的支座位移与残余位移减小量明显大于墩底弯矩增加量。
3）脉冲型地震动使桥梁结构产生更强的地震响应，支座位移与残余位移明显大于非脉冲型地震动下的相应量，但Fe-SMA-DVFPB在两类地震动作用下均能够有效控制支座位移。
基金
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  • 国家自然科学基金项目(52078243)
  • 甘肃省重点研发计划项目(22YF7GA161)
文献
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2025年第45卷第3期
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doi: 10.13197/j.eeed.2025.0316
  • 接收时间：2024-05-09
  • 首发时间：2026-03-20
  • 出版时间：2025-06-30
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  • 收稿日期：2024-05-09
  • 修回日期：2024-10-17
基金
国家自然科学基金项目(52078243)
甘肃省重点研发计划项目(22YF7GA161)
作者信息
    1.兰州理工大学 土木工程学院，甘肃 兰州 730050
    2.中国建筑标准设计研究院有限公司，北京 100048

通讯作者:

韩建平（1970—），男，教授，博士，主要从事结构抗震与减震控制、结构健康监测与损伤诊断研究。E-mail：
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https://castjournals.cast.org.cn/joweb/dzgcygczd/CN/10.13197/j.eeed.2025.0316
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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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