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极限状态模糊性对地震易损性分析的影响研究:以钢筋混凝土框架结构为例

于晓辉 李越然 宋鹏彦 吕大刚

于晓辉, 李越然, 宋鹏彦, 吕大刚. 极限状态模糊性对地震易损性分析的影响研究:以钢筋混凝土框架结构为例[J]. 工程力学, 2021, 38(9): 89-99, 109. doi: 10.6052/j.issn.1000-4750.2020.08.0604
引用本文: 于晓辉, 李越然, 宋鹏彦, 吕大刚. 极限状态模糊性对地震易损性分析的影响研究:以钢筋混凝土框架结构为例[J]. 工程力学, 2021, 38(9): 89-99, 109. doi: 10.6052/j.issn.1000-4750.2020.08.0604
YU Xiao-hui, LI Yue-ran, SONG Peng-yan, LÜ Da-gang. EFFECT OF FUSSINESS AT LIMIT STATES ON SEISMIC FRAGILITY ANALYSIS: REINFORCED CONCRETE FRAME CASES[J]. Engineering Mechanics, 2021, 38(9): 89-99, 109. doi: 10.6052/j.issn.1000-4750.2020.08.0604
Citation: YU Xiao-hui, LI Yue-ran, SONG Peng-yan, LÜ Da-gang. EFFECT OF FUSSINESS AT LIMIT STATES ON SEISMIC FRAGILITY ANALYSIS: REINFORCED CONCRETE FRAME CASES[J]. Engineering Mechanics, 2021, 38(9): 89-99, 109. doi: 10.6052/j.issn.1000-4750.2020.08.0604

极限状态模糊性对地震易损性分析的影响研究:以钢筋混凝土框架结构为例

doi: 10.6052/j.issn.1000-4750.2020.08.0604
基金项目: 国家自然科学基金项目(51778198);黑龙江省优秀青年基金项目(YQ2020E023);河北省自然科学基金项目(E2017201221)
详细信息
    作者简介:

    于晓辉(1982−),男,辽宁人,副研究员,博士,硕导,主要从事地震易损性和概率风险分析的研究(E-mail: yxhhit@126.com)

    李越然(1999−),男,河南人,本科生,主要从事钢筋混凝土结构抗震性能研究(E-mail: PCMLYR@163.com)

    吕大刚(1970−),男,黑龙江人,教授,博士,博导,主要从事地震可靠性、易损性和鲁棒性研究(E-mail: ludagang@sina.com)

    通讯作者:

    宋鹏彦(1982−),女,黑龙江人,讲师,博士,硕导,主要从事结构抗震可靠度和地震倒塌研究(E-mail: songpengyan@sina.com)

  • 中图分类号: TU311

EFFECT OF FUSSINESS AT LIMIT STATES ON SEISMIC FRAGILITY ANALYSIS: REINFORCED CONCRETE FRAME CASES

  • 摘要: 合理定义不同极限状态的结构抗震能力是地震易损性分析的关键步骤。然而,极限状态的定义十分依赖工程经验,包含较强的“模糊性”。为此,有必要针对极限状态模糊性对地震易损性的影响开展全面分析。考虑10种隶属函数来描述极限状态的模糊性,考虑不同模糊度的影响,以4个不同高度不同设防烈度的钢筋混凝土框架结构为例,开展了考虑极限状态模糊性的地震易损性分析,采用模糊-概率积分方法推导获得了不同隶属函数对应的地震易损性函数。对比考虑与不考虑极限状态模糊性的地震易损性分析结果,研究了在极限状态模糊性中考虑不同隶属函数和不同模糊度对地震易损性结果的影响,给出了考虑极限状态模糊性修正的地震易损性函数。分析结果表明:采用不同隶属函数考虑极限状态模糊性对地震易损性结果影响较为显著。随着模糊度的提高,不同隶属函数对应的考虑极限状态模糊性的地震易损性分析结果差异也逐渐增加。采用该文提出的考虑极限状态模糊性修正的地震易损性函数可以较好地体现极限状态模糊性对地震易损性的影响。
  • 图  1  经典集合论与模糊集合论中的隶属度含义差异

    Figure  1.  Difference between memberships defined according to the classic sets and the fuzzy sets

    图  2  本文考虑的10种隶属函数

    Figure  2.  Ten membership functions considered in this paper

    图  3  隶属度函数的模糊形状参数的定义

    Figure  3.  Definition of fuzziness shape factor of membership functions

    图  4  算例结构 /mm

    Figure  4.  Case structures

    图  5  考虑和不考虑极限状态模糊性的地震易损性曲线

    Figure  5.  Seismic fragility curves with and without considering fuzziness in limit states

    图  6  λ值对考虑极限状态模糊性的地震易损性的影响

    Figure  6.  Effect of λ values on seismic fragility curves considering fuzziness in limit states

    图  7  隶属函数对考虑模糊性的地震易损性的影响

    Figure  7.  Effect of membership on seismic fragility considering fuzziness in limit states

    图  8  10种隶属函数对应的ηP值及其随λ的变化

    Figure  8.  Values of ηP corresponding to ten membership considered and the corresponding variation with λ

    图  9  ${m'_R}$${\beta '_R}$λ的关系

    Figure  9.  Relationships between ${m'_R}$ and ${\beta '_R}$ and λ

    表  1  10种隶属函数的形状参数γ

    Table  1.   Calculated shape factors γ of ten membership functions

    μi(x)μ1(x)μ2(x)μ3(x)μ4(x)μ5(x)μ6(x)μ7(x)μ8(x)μ9(x)μ10(x)
    γ1.0000.5000.3330.6670.3630.6360.5590.5570.4180.582
    下载: 导出CSV

    表  2  考虑极限状态模糊性的地震易损性函数系数

    Table  2.   Parameters of seismic fragility functions considered limit state fuzziness

    系数隶属函数
    μ1(x)μ2(x)μ3(x)μ4(x)
    α1−1/2−(λ−1)/2λ1−1
    α2−1/2−(λ+1)/2λ−(1−λ)2/2(1−λ)2/2
    α3a1/2λ−(1+λ)2/2(1−λ)2/2
    α4a1/2λ−2 a12a1
    α5(1−λ) a1a1
    α6(1+λ) a1a1
    α7a2a2
    α8a2/2 a2/2
    α9a2/2 a2/2
    β1β1+ln(1−λ)/σln tμln t/σln t
    β2β1+ln(1+λ)/σln tβ1+ln(1−λ)/σln t
    β3β1σln tβ1+ln(1+λ)/σln t
    β4β2σln tβ1σln t
    βi=5~9βi−3σln t
    注:${a_1} = [\exp ( - {\mu _{\ln t}} + \sigma _{\ln t}^2/2)]$, ${a_2} = \exp [2( - {\mu _{\ln t}} + \sigma _{\ln t}^2)]$。
    下载: 导出CSV

    表  3  概率地震需求模型参数

    Table  3.   Probabilistic seismic demand model parameters

    参数结构
    F-1F-2F-3F-4
    β0−3.91−3.75−3.75−3.60
    β10.820.890.780.79
    ${\beta _{D|{S_{\rm{a}}}}} $0.400.370.380.35
    下载: 导出CSV

    表  4  概率抗震能力模型参数

    Table  4.   Probabilistic seismic capacity model parameters

    结构极限状态θmax/(%)
    轻微破坏中等破坏严重破坏完全破坏
    mCβCmCβCmCβCmCβC
    F-10.210.310.680.071.250.183.770.26
    F-20.230.160.730.051.420.082.540.15
    F-30.300.100.750.081.700.174.070.16
    F-40.260.090.660.102.000.123.210.27
    下载: 导出CSV

    表  5  基于ηP的隶属函数形状对地震易损性影响等级划分

    Table  5.   Classification of effect of membership functions on seismic fragility curves using ηP

    影响等级${\eta _{\rm P}}$
    0%~1%
    1%~5%
    III5%~10%
    IV10%~15%
    V>15%
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-08-26
  • 修回日期:  2020-11-16
  • 网络出版日期:  2021-03-04
  • 刊出日期:  2021-09-13

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