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Article(id=1241794073430921305, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241794070289387562, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2025.0518, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1723996800000, receivedDateStr=2024-08-19, revisedDate=1732982400000, revisedDateStr=2024-12-01, acceptedDate=null, acceptedDateStr=null, onlineDate=1773996378524, onlineDateStr=2026-03-20, pubDate=1761062400000, pubDateStr=2025-10-22, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773996378524, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773996378524, creator=13701087609, updateTime=1773996378524, updator=13701087609, issue=Issue{id=1241794070289387562, tenantId=1146029695717560320, journalId=1241701559352995854, year='2025', volume='45', issue='5', pageStart='1', pageEnd='227', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1773996377775, creator=13701087609, updateTime=1773996935444, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241796409465307627, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241794070289387562, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241796409465307628, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241794070289387562, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=193, endPage=207, ext={EN=ArticleExt(id=1241794075016368241, articleId=1241794073430921305, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Evaluation of seismic performance of RC beam-column connections considering non-uniform freeze-thaw damage, columnId=1241794071602200899, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

The freeze-thaw cycle (FTC) is one of a major factors leading to the damage of reinforced concrete (RC) structures in severely cold regions. The seismic performance evaluation of FTC-damaged RC beam-column connections is critical to the assessment of structural safety. However, the studies on the seismic performance evaluation of FTC-damaged RC beam-column connections under severe cold environments are still scarce. In this study, the influences of freeze-thaw cycles (N) and axial force ratio (n) on the seismic performance of RC beam-column connections are deeply investigated. Based on the test results, a calculation model of the shear force-strain envelope curve of RC connections that integrates the effects of the inhomogeneous temperature field distribution and axial compression ratio was established. The results show that with the increase of NFTCs, the bearing capacity of the RC connections and the shear bearing capacity of the core area decrease, while the ductility, shear strain γ, and shear deformation to the total deformation ΔPZ/Δ gradually increase, and after 300 freeze-thaw cycles, ΔPZ/Δ is up to 21.90%. The established shear force-distortion calculation model for the FTC-damaged RC core area can accurately calculate the shear force Vjh and shear distortion γ. The mean error of both the shear force Vjh and shear distortion γ does not exceed 20%, and the standard deviation does not exceed 0.1. Furthermore, the precision of Vjh is slightly higher than that of γ. The shear skeleton curve calculation model established can be used to evaluate the seismic performance of FTC-damaged RC beam-column connections under earthquake actions.

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在严寒地区,冻融循环（freeze-thaw cycle, FTC）是导致钢筋混凝土（reinforced concrete, RC）结构破坏的主要因素之一。冻融损伤后的RC梁柱节点的抗震性能评估对于结构安全性至关重要。然而,有关严寒环境下冻损伤RC梁柱节点抗震性能评估的研究却很少。该文深入探究了冻融循环次数（NFTCs）和轴压比（n）对RC梁柱节点抗震性能的影响,并在试验研究的基础上建立了综合考虑不均匀温度场分布和轴压比影响的冻损RC梁柱节点核心区剪力-剪应变计算模型。研究结果表明：随着NFTCs的增加, RC节点的峰值荷载与核心区的抗剪承载力均下降,而节点延性与剪应变γ以及剪切变形占总变形的比例ΔPZ/Δ逐渐增加,且在经历300次NFTCs后节点核心区的ΔPZ/Δ高达21.90%；所建立的冻损RC梁柱节点核心区剪力-剪应变计算模型能够准确计算剪力Vjh和剪应变γ,其平均误差不超过20%,标准偏差不超过0.1。该文所建立的剪切骨架曲线计算模型可用于冻融损伤RC梁柱节点的抗震性能评估。

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程小珊（1987—）,女,讲师,硕士,主要从事结构工程与工程管理研究。E-mail：

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3.同济大学土木工程学院,上海200092, bio={"content":"

程小珊（1987—）,女,讲师,硕士,主要从事结构工程与工程管理研究。E-mail：

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程小珊（1987—）,女,讲师,硕士,主要从事结构工程与工程管理研究。E-mail：

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journalId=1241701559352995854, articleId=1241794073430921305, language=CN, orderNo=2, keyword=钢筋混凝土梁柱节点), Keyword(id=1241802965149880470, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794073430921305, language=CN, orderNo=3, keyword=抗震性能评估), Keyword(id=1241802965267320986, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794073430921305, language=CN, orderNo=4, keyword=剪切骨架曲线计算模型)], refs=[Reference(id=1241802969474208031, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794073430921305, doi=null, pmid=null, pmcid=null, year=2008, volume=29, issue=4, pageStart=10, pageEnd=19, url=null, language=null, rfNumber=[1], rfOrder=0, authorNames=李宏男, 肖诗云, 霍林生, journalName=建筑结构学报, refType=null, unstructuredReference=李宏男，肖诗云，霍林生．汶川地震震害调查与启示[J]．建筑结构学报, 2008, 29(4): 10-19., articleTitle=汶川地震震害调查与启示, refAbstract=null), Reference(id=1241802969541316896, tenantId=1146029695717560320, journalId=1241701559352995854, 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注：Vc—开裂剪力；γc—开裂应变；Vy—屈服剪力；γy—屈服应变；Vp—峰值剪力；γp—峰值应变；Vr—残余剪力；γr—残余应变；Vr=0.2Vp。

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Design parameters of test specimens

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试件编号NFTCsFTCs时间/d轴压比n剪压比Vjh/fcbjhj配箍率ρshfyv/fc
JD-1000.1910.2080.030
JD-2100230.1910.2080.030
JD-3200460.1910.2080.030
JD-4300690.1910.2080.030
JD-7200460.0510.2080.030
JD-8200460.3320.2080.030
), ArticleFig(id=1241802968798925078, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794073430921305, language=CN, label=表1, caption=

试件设计参数

, figureFileSmall=null, figureFileBig=null, tableContent=
试件编号NFTCsFTCs时间/d轴压比n剪压比Vjh/fcbjhj配箍率ρshfyv/fc
JD-1000.1910.2080.030
JD-2100230.1910.2080.030
JD-3200460.1910.2080.030
JD-4300690.1910.2080.030
JD-7200460.0510.2080.030
JD-8200460.3320.2080.030
), ArticleFig(id=1241802968866033943, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794073430921305, language=EN, label=Table 2, caption=

Calculation results for Vjh and γ

, figureFileSmall=null, figureFileBig=null, tableContent=
编号混凝土强度fcuNFTCs轴压比n开裂点屈服点峰值点残余点
剪力剪应变剪力剪应变剪力剪应变剪应变
JD-155.0800.191175.8130.026238.8890.057359.8190.1640.445
JD-255.081000.191155.1370.031228.2300.074342.9250.2550.639
JD-355.082000.191135.969∗0.024214.323∗0.092323.141∗0.3650.856
JD-455.083000.191122.0800.037∗192.2570.111316.7700.5301.145
JD-532.003000.191102.6090.015155.3070.080273.3000.432∗1.098∗
JD-640.33000.191111.6130.023172.5970.080∗294.7390.5271.073
JD-755.082000.051134.4840.026193.7080.073303.5140.5141.173
JD-855.082000.332110.1350.019201.9760.071200.6690.3140.854
JD-932.0000.191141.2870.010210.6960.039350.8210.1120.378
JD-1032.001000.191123.592∗0.011200.328∗0.052332.843∗0.1800.555
JD-1132.002000.191106.9500.012187.1370.065311.9520.2630.758
JD-1240.3000.191160.4500.013219.7650.040364.3930.1540.400
JD-1340.301000.191140.9310.014209.5760.053346.6420.2430.581
JD-1440.302000.191122.7990.016∗196.4800.066325.9240.3500.785
JD-1555.0800.051160.8160.024219.6530.064344.0880.2710.588
JD-1655.081000.051147.2020.025208.2130.068325.2760.3820.863
JD-1755.083000.051125.4370.031169.5950.077∗272.8940.7151.586∗
JD-1855.0800.332168.3650.012227.6590.041352.0770.1140.357
JD-1955.081000.332151.9280.014216.3330.056331.5740.2050.591
JD-2055.083000.332125.6510.023178.1070.087274.4880.476∗1.203
), ArticleFig(id=1241802968987668762, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794073430921305, language=CN, label=表2, caption=

V jh和γ的计算结果

, figureFileSmall=null, figureFileBig=null, tableContent=
编号混凝土强度fcuNFTCs轴压比n开裂点屈服点峰值点残余点
剪力剪应变剪力剪应变剪力剪应变剪应变
JD-155.0800.191175.8130.026238.8890.057359.8190.1640.445
JD-255.081000.191155.1370.031228.2300.074342.9250.2550.639
JD-355.082000.191135.969∗0.024214.323∗0.092323.141∗0.3650.856
JD-455.083000.191122.0800.037∗192.2570.111316.7700.5301.145
JD-532.003000.191102.6090.015155.3070.080273.3000.432∗1.098∗
JD-640.33000.191111.6130.023172.5970.080∗294.7390.5271.073
JD-755.082000.051134.4840.026193.7080.073303.5140.5141.173
JD-855.082000.332110.1350.019201.9760.071200.6690.3140.854
JD-932.0000.191141.2870.010210.6960.039350.8210.1120.378
JD-1032.001000.191123.592∗0.011200.328∗0.052332.843∗0.1800.555
JD-1132.002000.191106.9500.012187.1370.065311.9520.2630.758
JD-1240.3000.191160.4500.013219.7650.040364.3930.1540.400
JD-1340.301000.191140.9310.014209.5760.053346.6420.2430.581
JD-1440.302000.191122.7990.016∗196.4800.066325.9240.3500.785
JD-1555.0800.051160.8160.024219.6530.064344.0880.2710.588
JD-1655.081000.051147.2020.025208.2130.068325.2760.3820.863
JD-1755.083000.051125.4370.031169.5950.077∗272.8940.7151.586∗
JD-1855.0800.332168.3650.012227.6590.041352.0770.1140.357
JD-1955.081000.332151.9280.014216.3330.056331.5740.2050.591
JD-2055.083000.332125.6510.023178.1070.087274.4880.476∗1.203
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考虑不均匀冻融损伤RC梁柱节点抗震性能评估
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程小珊 1, 3 , 徐丽 2 , 郄亚微 1
地震工程与工程振动 | 研究论文 2025,45(5): 193-207
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地震工程与工程振动 | 研究论文 2025, 45(5): 193-207
考虑不均匀冻融损伤RC梁柱节点抗震性能评估
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程小珊1, 3 , 徐丽2, 郄亚微1
作者信息
  • 1.广安职业技术学院建筑工程学院,四川广安638000
  • 2.四川水利职业技术学院,四川崇州611231
  • 3.同济大学土木工程学院,上海200092

    • 程小珊（1987—）,女,讲师,硕士,主要从事结构工程与工程管理研究。E-mail：

Evaluation of seismic performance of RC beam-column connections considering non-uniform freeze-thaw damage
Xiaoshan CHENG1, 3 , Li XU2, Yawei QIE1
Affiliations
  • 1.School of Architectural Engineering, Guang’an Vocational Technical College, Guang’an 638000, China
  • 2.Sichuan Water Conservancy Vocational College, Chongzhou 611231, China
  • 3.College of Civil Engineering, Tongji University, Shanghai 200092, China
出版时间: 2025-10-22 doi: 10.13197/j.eeed.2025.0518
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摘要
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在严寒地区,冻融循环（freeze-thaw cycle, FTC）是导致钢筋混凝土（reinforced concrete, RC）结构破坏的主要因素之一。冻融损伤后的RC梁柱节点的抗震性能评估对于结构安全性至关重要。然而,有关严寒环境下冻损伤RC梁柱节点抗震性能评估的研究却很少。该文深入探究了冻融循环次数（NFTCs）和轴压比（n）对RC梁柱节点抗震性能的影响,并在试验研究的基础上建立了综合考虑不均匀温度场分布和轴压比影响的冻损RC梁柱节点核心区剪力-剪应变计算模型。研究结果表明：随着NFTCs的增加, RC节点的峰值荷载与核心区的抗剪承载力均下降,而节点延性与剪应变γ以及剪切变形占总变形的比例ΔPZ/Δ逐渐增加,且在经历300次NFTCs后节点核心区的ΔPZ/Δ高达21.90%；所建立的冻损RC梁柱节点核心区剪力-剪应变计算模型能够准确计算剪力Vjh和剪应变γ,其平均误差不超过20%,标准偏差不超过0.1。该文所建立的剪切骨架曲线计算模型可用于冻融损伤RC梁柱节点的抗震性能评估。

冻融损伤  /  钢筋混凝土梁柱节点  /  抗震性能评估  /  剪切骨架曲线计算模型

The freeze-thaw cycle (FTC) is one of a major factors leading to the damage of reinforced concrete (RC) structures in severely cold regions. The seismic performance evaluation of FTC-damaged RC beam-column connections is critical to the assessment of structural safety. However, the studies on the seismic performance evaluation of FTC-damaged RC beam-column connections under severe cold environments are still scarce. In this study, the influences of freeze-thaw cycles (N) and axial force ratio (n) on the seismic performance of RC beam-column connections are deeply investigated. Based on the test results, a calculation model of the shear force-strain envelope curve of RC connections that integrates the effects of the inhomogeneous temperature field distribution and axial compression ratio was established. The results show that with the increase of NFTCs, the bearing capacity of the RC connections and the shear bearing capacity of the core area decrease, while the ductility, shear strain γ, and shear deformation to the total deformation ΔPZ/Δ gradually increase, and after 300 freeze-thaw cycles, ΔPZ/Δ is up to 21.90%. The established shear force-distortion calculation model for the FTC-damaged RC core area can accurately calculate the shear force Vjh and shear distortion γ. The mean error of both the shear force Vjh and shear distortion γ does not exceed 20%, and the standard deviation does not exceed 0.1. Furthermore, the precision of Vjh is slightly higher than that of γ. The shear skeleton curve calculation model established can be used to evaluate the seismic performance of FTC-damaged RC beam-column connections under earthquake actions.

freeze-thaw damage  /  RC beam-column connection  /  seismic performance evaluation  /  calculation model of shear skeleton curve
程小珊, 徐丽, 郄亚微. 考虑不均匀冻融损伤RC梁柱节点抗震性能评估. 地震工程与工程振动, 2025 , 45 (5) : 193 -207 . DOI: 10.13197/j.eeed.2025.0518
Xiaoshan CHENG, Li XU, Yawei QIE. Evaluation of seismic performance of RC beam-column connections considering non-uniform freeze-thaw damage[J]. Earthquake Engineering and Engineering Dynamics, 2025 , 45 (5) : 193 -207 . DOI: 10.13197/j.eeed.2025.0518
正文
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0　引言
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节点是梁和柱的传力枢纽,是影响钢筋混凝土（reinforced concrete, RC）结构抗震性能的关键部位[1-2]。在地震作用下,一旦节点发生破坏即意味着与之相连的梁和柱同时失效,将产生灾难性的后果[3-4]。可见,对RC节点的抗震性能展开深入研究,建立其科学的抗震性能评估模型,减少人员伤亡与经济损失,具有显著意义。鉴于此,在过去的四十年里,诸多学者对RC节点的抗震性能展开了大量的研究[5-7]。研究明确了在地震作用下节点从起始受力状态下就存在斜压杆机构、桁架机构以及约束机构3种机构[5-7]。但以往的研究均局限于完好节点,未能考虑冻害问题对节点抗震性能的影响。
冻融循环（freeze-thaw cycle, FTC）作为混凝土耐久性破坏的三大因素之一,20世纪40年代就备受各国学者的关注[8-17]。起初,学者关于冻害问题的焦点在于混凝土冻融损伤机理方面[8-9],且一致认为混凝土内部孔隙率（毛细孔）是造成冻融损伤的最主要因素。之后,各国学者认识到混凝土作为一种工程材料, FTC导致其性能的劣化归结到底还是力学性能的劣化。所以后来关于混凝土材料在FTC后力学性能的研究则浩如烟海[10-11]。材料层面的FTC研究一致认为, FTC作用削弱了混凝土的力学性能包括弹性模量、抗压强度以及抗拉强度,钢筋与混凝土之间的黏结强度[10-11],且削弱的程度与冻融损伤程度成正比。影响冻融损伤程度的因素包括冻融循环次数（NFTCs）、混凝土强度以及试件内部温度场分布（冻融损伤是不均匀分布的[12-13]）。不能简单地以NFTCs表征冻融损伤程度,这导致了已有的诸多材料层面的冻融研究成果无法对比验证。混凝土动弹模量损失量D可表征冻融损伤程度的诸多影响因素,因此被广泛学者[12-13]认为是可定量化表征冻融损伤程度的优良指标。郑山锁等[13]以D作为表征冻融损伤程度的物理指标,在蔡昊模型[14]的基础上,建立了考虑混凝土结构内部不均匀分布温度场的冻融损伤模型。研究为RC构件层面冻融损伤程度的评估奠定了基础。
随着科技水平的提高,近年来,一些学者逐渐对构件层面的冻融展开了研究。探究重心由静力作用下RC构件的弯曲性能[15]、剪切性能[16]逐渐转为地震作用下的抗震性能[17]。冻融作用下RC构件抗震性能的研究包括RC梁、RC柱、再生混凝土柱以及RC剪力墙。服役中的RC梁、柱、节点大多处在相同的环境中。然而,关于FTC作用下RC梁柱节点抗震性能评估的研究则依然处于空白,仅郑捷等[6]对冻融循环下RC节点的抗震性能进行了初步的试验探究,但其也并未对展开定性的抗震性能评估。
综上,本文在已有研究[6]的基础上,从滞回性能、骨架曲线、剪切性能方面深入探究了冻融循环次数和轴压比对RC梁-柱节点抗震性能的影响,基于试验研究结果建立了综合考虑不均匀温度场分布和轴压比影响的冻融损伤RC梁柱节点剪力-剪应变骨架曲线计算模型。研究可用于冻融损伤RC梁柱节点的抗震性能评估。
1　试验概况
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1.1　试件设计
设计制作了几何构造与配筋均相同的6根RC梁-柱节点测试试件,以探究冻融循环作用下RC梁-柱节点的抗震性能,试件参数设计见表1[6]。由于人工气候模拟室尺寸的限制,无法对全尺寸RC梁柱节点进行FTC试验。与此同时,现有的有关冻融损伤RC构件的拟静力试验的研究都是采用的缩尺试件[6,12,15-17]。鉴于此,依据标准GB/T 50010—2010[18],以1∶2缩尺比例设计了6个配筋细节（相同的配筋率）、混凝土强度均与原型结构（5层RC框架结构）相同的RC梁柱节点试件。梁截面尺寸为150 mm×200 mm,柱截面尺寸为200 mm×200 mm。箍筋为HPB300,直径6 mm,实测屈服强度为270 MPa,弹性模量为2.1×105。柱端和梁端用箍筋加密以防止局部挤压,箍筋间距为30 mm,其余箍筋间距均为60 mm。钢筋混凝土梁柱节点的详细钢筋和尺寸见图1。更为详细的设计参见文献[6]。
节点的设计混凝土强度等级为C50,实测立方体抗压强度fcu为55.08 MPa。由于中国早期标准[18]没有考虑严寒地区结构的耐久性设计,因此设计的节点没有添加引气剂。试件浇筑后在经过28 d标准养护后,参考规范[19]将梁柱节点在室温下的水中浸泡一周,然后转移到人工气候模拟实验室进行FTC测试。在达到设计的NFTC后,对其施加低循环载荷[6]。
1.2　FTC测试
通过控制人工气候模拟实验室内的温度,可以重现冻融环境中的FTC过程。人工气候实验室的主要技术指标见[6,19],见图2。中国标准GB/T 50882—2009《普通混凝土长期性能和耐久性能试验方法标准》[19]中关于冷冻和融化温度范围的规定是：加热温度为15~20℃；冷却温度为（-20）~（-15）℃。鉴于此,加热期间的最高温度设置为15℃,冷却期间的最低温度设置为-17℃。冷却速率设置为16℃/h,加热速率设置为32℃/h。FTC设置见图2[6,19]。
1）控制方式：通过编程控制喷洒时间、湿度以及温度指标,实施在线监测。
2）湿度控制：空载状态下的湿度变化范围为30%~98%RH；当湿度变化范围在30%~75%RH时,湿度偏离-5%~+5%；当湿度波动范围在75%~98%时,湿度偏差为-3%~+2%。
3）温度控制：温度偏差为-2℃~+2℃,温度波动值≤±0.5℃。
4）人工喷洒：垂直向下,降水量10~15 cm/h（可调）,降雨时间1 min~100 h（可调节）。
1.3　拟静力测试
加载系统和测点布局见图3所示。首先,通过液压千斤顶施加轴向压力至设计轴压比n（n值见表1）,并在循环加载期间保持恒定。通过监测液压千斤顶的读数实现恒定轴压力,见图4。然后施加水平往复载荷。加载点距离柱上端105 mm,详细测点布置见图1。采用荷载-位移混合荷载方案。屈服前采用荷载控制,荷载增量为5 kN。屈服后,采用位移控制。荷载控制期间循环1次,位移控制期间循环3次[6]。具体加载历程见图4。循环荷载的停机条件是试件载荷降至峰值载荷的80%,或者试件严重失效。
2　结果分析
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2.1　滞回曲线
各节点试件柱顶水平荷载-位移滞回曲线见图5。由图可知,6个节点的滞回性能大体一致：屈服前,滞回曲线近似呈斜直线,无明显刚度退化；屈服后,加卸载刚度退化逐渐显著,残余位移逐渐明显；峰值后,残余位移进一步显著,致使滞回环形状向“反弓形”变化。
2.2　骨架曲线
骨架曲线特征点标定方法见图6。所有试件的骨架曲线见图7。由图6与图7可知,骨架曲线各特征点参数随NFTCs与n的变化见图8。由图7~图8可知,随着NFTCs的增加,试样的开裂载荷、屈服载荷和峰值载荷均逐渐降低。然而极限位移与延性却呈现出略微增大的变化,这与RONG等[17]、XU等[20]的研究相反。通常情况下,节点的性能会因为FTC而恶化。然而试验结果中极限位移与延性却呈现出略微增大的变化。这是因为FTC作用在加载前期时显著降低了梁端纵向钢筋与核心区的黏结性能,而最终残余的黏结强度随NFTCs的增加呈增加趋势。因此,在节点加载初期,致使RC梁柱节点核心区的破坏类型由混凝土强度主控制的“斜压型”剪切破坏向梁纵筋在其连通的核心区的黏结退化转变,并且在加载后期的较大位移下可恢复部分荷载。在节点加载后期,相对较大的残余黏结强度导致“桁架机构”传进核心区域的剪力增加,“斜压杆机构”传进核心区域的剪力降低；致使核心区内混凝土承受到的斜向压应力降低,“斜压”破坏的发生逐渐推迟,节点的极限变形与屈服变形之差提高,极限位移与延性系数略微增加。开裂状态之前,不同NFTCs下节点的刚度接近；开裂状态之后节点的刚度显著降低。节点峰值后刚度和NFTCs之间的关系如式（1）所示：
现有研究[21]结果表明,轴压比可以提高RC构件的峰值荷载,降低其变形能力。而本研究发现,冻融损伤节点的峰值荷载随着轴压比的增加而逐渐降低。这是由于设计节点核心区的剪压比已是中高水平（0.208,经过200次冻融循环后混凝土强度降低,节点实际剪压比将增大）,在中高水平下斜压杆机构中的斜向压力已较大；随轴压比n的提高,节点核心区斜压杆机构中的压力得到了进一步提高,导致斜压杆中的压力提前企及了混凝土压溃能力。
2.3　剪切性能
2.3.1　剪应变γ
在试验中,通过核心区的对角线长度变化来测量不同加载条件下的连接核心区的剪切变形γ,见图9（a）,对应的节点受力分析见图9（b）、（c）。核心区剪切变形γ的表达式为
式中：h为梁截面有效高度；b为柱截面有效宽度；为对角线方向的平均变位,按式（3）计算：
式中,δ1+δ′1、δ2+δ′2分别为布置在核心区的交叉位移计量测的伸长值与压缩值。
核心区剪应变γ诱发的柱顶变形Δpz即剪切成分引起的节点变形：
式中：H为试件高度；L为试件宽度。
核心区剪应变γ诱发的柱顶变形占柱顶总变形Δ的比ΔPZ/Δ,即
实测剪切变形γ和剪切位移占比的ΔPZ/Δ变化,见图10。虽然节点核心区被梁和柱包围,其处于单边冻融较梁、柱（三边冻融）受FTC的影响小,但随着NFTCs的增加,γ和ΔPZ/Δ仍逐渐增加。这是由于受FTCs后混凝土的力学性能恶化造成的。
尽管剪应变γ随着n的增加而减小,但剪切变形与总变形之比ΔPZ/Δ却呈现出上升趋势。这主要是因为轴压比使节点的总变形明显减少所致（图8）。
2.3.2　剪力Vjh
取柱的脱离体见图9（b）。图中Vc为柱端剪力,由力的平衡得柱端剪力等于柱顶水平力P；Csl、Csr分别为梁端受压侧纵筋压力；Tbr、Tbl为梁端受拉侧纵筋所受拉力；Ccl、Ccr分别为梁端受压侧混凝土压力。
由图9（b）弯矩平衡（考虑P-Δ效应）条件有：
由图9（c）隔离体力的平衡可得：
依据梁截面受压侧合力的大小等于受拉侧钢筋拉力的大小,则
联立式（6）~式（8）可得：
由式（9）得到RC节点核心区剪力Vjh。剪力Vjh随参数的变化规律见图11。随NFTCs的增加,核心区剪力逐渐减小,呈现出与节点承载能力相同的变化规律。当轴压比从0.051逐渐增加到0.332时,核心区的剪力先增加然后减少,整体呈现出减小的变化趋势。
开裂、屈服、峰值下因P-Δ效应诱导的剪切荷载占RC节点核心区总剪切荷载Vjh的比例,见图12。由图可知,因P-Δ效应诱导的剪切荷载占比与节点的冻损程度无显著相关关系。然而,值得指出的是峰值点处各试件因P-Δ诱导的核心区剪切荷载比例基本超过20%（JD-7除外）,所占比例较大。因此,在建立冻融损伤RC梁柱节点剪力计算模型时,应考虑轴压比的影响,此为下文的计算模型奠定了理论基础。
3　RC节点剪切骨架曲线模型
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RC节点核心区剪切骨架计算模型是RC节点核心区剪切恢复力模型的主要组成部分,准确建立其定量化计算公式具有重要意义。LOWES等[22]提出的四折线Pinching4滞回模型,见图13,能够较全面反映节点核心区的剪切滞回特性。因此,本文参考该模型建立节点核心区剪切骨架曲线计算模型（包含冻融节点和未冻融节点）。与此同时,考虑到严寒环境下冻融损伤RC节点中混凝土力学性能劣化对其抗剪性能影响机理非常复杂,采用理论方法难以进行准确表征。因此,本文首先参考HASELTON等[23]的模型,并考虑斜压杆应力扩散现象,给出了未冻融RC节点核心区剪切骨架曲线计算公式。进而依据前述冻融损伤RC节点的实测结果,通过多参数回归分析,构建了综合考虑冻融损伤程度与轴压比影响的RC节点核心区剪切骨架曲线计算公式,详细建立过程见图13。
3.1　未冻融RC节点
为准确表征RC节点剪切破坏全过程的受剪性能, HASELTON等[23]提出了基于斜压杆模型的节点剪切骨架曲线计算公式,取得了良好的计算精度并有效地简化了计算流程。因此,本文参考MITRA等[23]提出的模型,并考虑斜压杆应力扩散现象,定量化标定了未冻融RC节点剪切骨架曲线特征点的参数,具体如下。
1）斜压杆有效宽度
由圣维南原理可知,节点斜压杆中存在如图14（a）所示的应力扩散现象,因而斜压杆有效受压宽度大于其端部受压区宽度。由图14（a）可知,节点斜压杆的有效宽度wstruct为
式中：φ为应力扩散角度,取φ=26.5°[23]；lsp为应力扩散长度,取lsp=l/6[23],l为节点斜压杆长度[23]；cb、cc分别为梁截面、柱截面的受压区高度,分别按式（11）、式（12）计算确定；hb、hc分别为梁截面、柱截面高度；N为柱受到的轴向压力；Ac为柱截面面积；fc为混凝土抗压强度。
2）剪力传递机制
斜压杆模型中假定核心区剪力均匀分布且仅通过斜压杆传递,则根据静力平衡关系可知,核心区剪力为
式中：bj为节点核心区有效宽度；astruct为斜压杆与水平方向的夹角,其值取为arctan（hb/hc）；fc,struct为考虑混凝土软化效应及箍筋约束效应的斜压杆有效压应力,按式（14）计算确定。
式中：fc,mander为基于Mander混凝土本构模型[24]计算的节点约束混凝土压应力；εcc为约束混凝土峰值压应变；εt为斜压杆混凝土拉应变,根据开裂混凝土的平均应变摩尔圆（图14（b））可知：
式中εstruct为斜压杆压应变。
3）节点剪切变形
假定节点核心区仅发生剪切变形,则由图9（a）所示的节点斜压杆模型几何变形关系可知,斜压杆压应变εstruct可表示为
4）特征点的标定
基于计算式（10）~式（16）,通过编制MATLAB计算程序,计算得到了各未冻融节点剪切破坏全过程的剪力-剪切变形关系。进而依据图7和图13的特征参数标定方法,确定了未冻融节点的屈服特征点、峰值特征点、残余特征点的剪力和剪切变形。开裂点的确定如下。
节点开裂状态以核心区混凝土率先企及抗拉强度ft为表征。取核心区内部的微元体X为目标,其受力见图14（c）。依据微元体X（图14（c））在双向受力下斜截面主拉应力计算式,得核心区开裂时剪切应力最大τmax为
式中σc=N/bchc为柱端传输给核心区的轴应力；bc为柱截面宽度；σb为箍筋约束在核心区形成的应力,取压为正。
当核心区开裂时,由τmax可得核心区开裂剪力Vjc,即
式中hj为核心区截面有效高度。
节点的开裂剪力Vjc为
由于非预应力梁,其轴向力可近似为0；且开裂前核心区箍筋对混凝土约束作用可忽略不计即σb=0。鉴于此,式（19）转化为
式中：当σc≥0.5fc时,取σc=0.5fc；η为综合影响系数,其值取为0.67；φc为梁对节点约束参数,无正交梁节点取φc=1.0。
3.2　考虑不均匀分布温度场的冻融损伤模型D
郑山锁等[13,25-26]以混凝土动弹模量损失量D作为冻融损伤程度的物理指标,从冻损机理为出发点,基于蔡昊模型[14],综合试验结果与理论推导,提出了广泛适用的并可考虑混凝土结构内部不均匀分布温度场的冻融损伤模型,如式（21）所示：
式中：Vd为受冻融影响混凝土的体积；V为处于冻融环境中混凝土结构的体积；N为冻融循环次数；K为孔溶液在水泥浆体中的渗透参数的简写（m2）；η为孔溶液动力黏滞参数；Umax为单位体积水泥浆体内最大孔溶液结冰速率；dθ/dt（℃/s）为降温速率；更为详细的参数解释请见郑山锁等[13]的研究。
3.3　冻损RC节点
前述试验结果表明,严寒环境下冻融损伤RC节点的剪切骨架曲线形状与未冻融节点的类似,但其特征点参数将随冻融损伤程度和轴压比的变化而不断变化。因此,本文选取轴压比和冻损程度为参数,对完好试件核心区剪力-剪应变进行多参数修正,以建立严寒环境下冻融损伤RC节点核心区剪切骨架曲线参数计算方法,相应修正公式如式（22）、式（23）所示：
式中：V′i、γ′i为冻融损伤RC节点核心区剪切骨架曲线特征点i的剪力和剪应变；Vi、γi为未冻融RC节点核心区剪切骨架曲线特征点i的剪力和剪应变；fi（D,n）、gi（D,n）为综合考虑不均匀温度场分布的冻融损伤参数D与轴压比n影响的节点核心区特征点剪力和剪应变修正函数。
将冻融损伤RC节点核心区剪力和剪应变分别除以相同条件下未冻融节点核心区的剪力和剪应变,从而得到各试件不同特征状态下的剪力和剪应变修正系数随冻融损伤程度D和轴压比n的变化规律,见图15~图16。值得指出的是,为保证文章所建剪切骨架曲线模型的准确性,在建立过程中加入了同一批次的14个RC节点试件。由图15~图16可知,随D的增大,节点核心区不同特征点的剪力修正系数逐渐减小,剪应变修正系数则呈增大趋势。不同轴压比节点核心区各特征点的剪力和剪应变修正系数近似呈线性变化关系。鉴于此,将冻融损伤RC节点核心区不同特征点的剪力和剪应变修正函数fi（D,n）、gi（D,n）假定为关于轴压比n和冻融损伤程度D的二次函数形式,并考虑边界条件得到相应的表达式如式（24）、式（25）所示：
式中,a、b、c、d、e、f均为拟合参数,其值多参数回归分析得到,具体分析结果见图17。其中,为了确保多参数回归计算公式的准确性,在回归计算时随机选择2个试件（表2）的特征点数据不参与多参数非线性曲面回归分析,而仅用于验证计算模型的准确性。至此,得到冻融损伤RC节点核心区剪切骨架曲线计算公式如式（26）~式（33）所示。
开裂剪力V′c和剪应变γ′c,如式（26）、式（27）所示：
屈服剪力V′y和剪应变γ′y,如式（28）、式（29）所示：
峰值剪力V′p和剪应变γ′p,如式（30）、式（31）所示：
残余剪力V′u和剪应变γ′u,如式（32）、式（33）所示：
3.4　准确性验证
由3.1节~3.3节所提出的未冻融与冻损RC节点剪切骨架曲线模型可计算出各RC节点核心区剪力Vjh和剪切应变γ,相应计算结果见表2。图18（a）~（b）是20个RC节点骨架曲线特征点的剪力Vjh和剪切变形γ的计算结果与试验结果的对比。由图18（a）~（b）可知,Vjh和γ的计算结果是准确的,平均误差不超过20%,标准偏差不超过0.1。一些节点的剪切变形γ计算误差较大,其原因可以归结为FTC作用的不确定性和混凝土材料本身的可变性[10-12,26-28]。
4　结论
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本文深入研究了NFTCs和n对RC梁柱节点抗震性能的影响,并根据试验结果建立了RC节点核心区剪切骨架曲线计算模型,得出如下主要结论：
1）通常情况下,由于FTCs的作用,构件的性能会变差。然而,冻融损伤节点的延性却略有增加。与此同时,随NFTCs的增加, RC节点的峰值荷载与核心区的抗剪承载力均下降,而γ和ΔPZ/Δ逐渐增加,且300次NFTCs后节点核心区的ΔPZ/Δ高达21.90%。因此,在评估冻融环境下在役RC结构的抗震性能时,不能忽视节点核心区的剪切变形对整体结构水平位移的影响。
2）对于没有受到FTC作用的节点,柱顶承载能力通常随着轴力比n的增加而增加。然而,当Vjh/fcbjhj大于0.208时,轴力比n的增加将导致冻融损伤RC节点核心区的承载能力、变形能力和剪切变形下降。
3）结合四折线Pinching4模型与Mitra模型,考虑斜压杆应力扩散现象,建立了未冻融RC节点核心区剪切骨架曲线理论计算公式。
4）提出了一个综合不均匀温度场分布和轴压比影响的冻损RC梁柱节点剪力-剪应变计算模型,并对计算模型的精度进行了验证。结果表明,剪力Vjh和剪应变γ的平均误差不超过20%,标准偏差不超过0.1。
基金
收起
  • 国家自然科学面上项目(52278530)
  • 四川省教育厅人文社会科学重点研究基地项目(JGYQ2023025)
  • 广安市社科联课题(2019-45)
文献
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2025年第45卷第5期
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文章信息
doi: 10.13197/j.eeed.2025.0518
  • 接收时间：2024-08-19
  • 首发时间：2026-03-20
  • 出版时间：2025-10-22
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  • 收稿日期：2024-08-19
  • 修回日期：2024-12-01
基金
国家自然科学面上项目(52278530)
四川省教育厅人文社会科学重点研究基地项目(JGYQ2023025)
广安市社科联课题(2019-45)
作者信息
    1.广安职业技术学院建筑工程学院,四川广安638000
    2.四川水利职业技术学院,四川崇州611231
    3.同济大学土木工程学院,上海200092
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https://castjournals.cast.org.cn/joweb/dzgcygczd/CN/10.13197/j.eeed.2025.0518
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2种不同金属材料的力学参数
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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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