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Article(id=1244334017403793722, tenantId=1146029695717560320, journalId=1243988319449690156, issueId=1244334009858240758, articleNumber=null, orderNo=null, doi=10.19994/j.cnki.WEE.2025.0067, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1729353600000, receivedDateStr=2024-10-20, revisedDate=1736697600000, revisedDateStr=2025-01-13, acceptedDate=null, acceptedDateStr=null, onlineDate=1774601948357, onlineDateStr=2026-03-27, pubDate=1759248000000, pubDateStr=2025-10-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774601948357, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774601948357, creator=13701087609, updateTime=1774601948357, updator=13701087609, issue=Issue{id=1244334009858240758, tenantId=1146029695717560320, journalId=1243988319449690156, year='2025', volume='41', issue='4', pageStart='1', pageEnd='211', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1774601946558, creator=13701087609, updateTime=1774602401281, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244335917167657884, tenantId=1146029695717560320, journalId=1243988319449690156, issueId=1244334009858240758, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244335917167657885, tenantId=1146029695717560320, journalId=1243988319449690156, issueId=1244334009858240758, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=145, endPage=154, ext={EN=ArticleExt(id=1244334018288791889, articleId=1244334017403793722, tenantId=1146029695717560320, journalId=1243988319449690156, language=EN, title=Consideration of ground motion uncertainty in regional buildings damage simulation and probabilistic damage estimation, columnId=null, journalTitle=World Earthquake Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Ground motion has significant uncertainty, and different ground motion response spectra under the same amplitude have significant differences, which have a significant impact on the estimation of seismic damage to regional buildings. This study developed a regional building seismic damage simulation program suitable for multiple-story masonry and concrete frame structures, which can conveniently and quickly simulate regional buildings seismic damage under set earthquakes, and performed regional building damage simulations and probabilistic analysis with motion uncertainties. A typical urban region in Chifeng city was selected as the research area: 30 ground motions were selected to consider their uncertainty, and the ground motions amplitudes were modulated to the set intensity (0.05 g, 0.10 g, 0.20 g, and 0.40 g). Then seismic damage simulation of regional buildings under single and multiple seismic inputs were conducted respectively, the impact of seismic uncertainty on the seismic damage results of regional buildings was analyzed. Based on the seismic damage results under the set intensities, a probability density distribution model of regional buildings damage index based on Beta distribution was established. Results indicate that multiple seismic inputs take into account the uncertainty of seismic motion, which can more scientifically and objectively reflect the seismic damage situation of regional buildings; The established Beta distribution model can be used to estimate the post-earthquake damage of buildings in similar areas. The research results can provide reference for regional buildings safety assessment and seismic fortification.

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地震动具有较大不确定性，且同一幅值下不同地震动反应谱具有明显差异，对区域建筑震害估计结果影响显著。该研究开发了适用于多层RC框架结构和设防砌体结构的区域建筑震害模拟程序，可以方便快捷地进行设定地震下的区域建筑震害模拟，并基于此开展了考虑地震动不确定性的区域震害模拟和损伤概率估计。选取赤峰市主城区典型区域为研究区域，选择30条实际地震动作为地震动输入以考虑其不确定性，将地震动幅值分别调幅至设定烈度（0.05、0.10、0.20、0.40 g），分别开展单条和多条地震动输入下的区域建筑震害模拟，分析地震动不确定性对区域建筑震害结果的影响。根据设定烈度下的震害结果，建立了基于Beta分布的区域建筑损伤指数概率密度分布模型。研究结果表明：多条地震动输入考虑了地震动的不确定性，能够更加科学、客观地反映区域建筑的震害情况；建立的Beta分布模型，可以用于估计相似区域建筑的震后损伤情况。研究结果可为区域建筑安全评估和抗震设防等提供参考。

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王东明（1977—），男，研究员，博士，主要从事地震灾害风险评估、情景构建及震害仿真、震害预测等方面的研究。E-mail：
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滕菲（1986—），女，高级工程师，硕士，主要从事工程结构抗震研究。E-mail：

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滕菲（1986—），女，高级工程师，硕士，主要从事工程结构抗震研究。E-mail：

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滕菲（1986—），女，高级工程师，硕士，主要从事工程结构抗震研究。E-mail：

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(in Chinese), articleTitle=Disaster risk analysis based on ground motion parameters, refAbstract=null), Reference(id=1244335216765027274, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, doi=null, pmid=null, pmcid=null, year=2012, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[26], rfOrder=39, authorNames=李文博, journalName=null, refType=null, unstructuredReference=李文博. 基于IDA方法的RC框架结构地震易损性分析研究[D]. 西安: 西安建筑科技大学, 2012., articleTitle=基于IDA方法的RC框架结构地震易损性分析研究, refAbstract=null), Reference(id=1244335216853107665, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, doi=null, pmid=null, pmcid=null, year=2012, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[26], rfOrder=40, authorNames=LI Wenbo, journalName=null, refType=null, unstructuredReference=LI Wenbo. Study on seismic fragility analysis of RC frame structures based on the IDA method[D]. Xi’an: Xi’an University of Architecture and Technology, 2012. (in Chinese), articleTitle=Study on seismic fragility analysis of RC frame structures based on the IDA method, refAbstract=null), Reference(id=1244335216932799442, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, doi=null, pmid=null, pmcid=null, year=2017, volume=34, issue=1, pageStart=69, pageEnd=75, 100, url=null, language=null, rfNumber=[27], rfOrder=41, authorNames=于晓辉, 吕大刚, 范峰, journalName=工程力学, refType=null, unstructuredReference=于晓辉, 吕大刚, 范峰. 基于易损性指数的钢筋混凝土框架结构地震损伤评估[J]. 工程力学, 2017, 34(1): 69-75, 100., articleTitle=基于易损性指数的钢筋混凝土框架结构地震损伤评估, refAbstract=null), Reference(id=1244335217029268440, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, doi=null, pmid=null, pmcid=null, year=2017, volume=34, issue=1, pageStart=69, pageEnd=75, 100, url=null, language=null, rfNumber=[27], rfOrder=42, authorNames=YU Xiaohui, LÜ Dagang, FAN Feng, journalName=Engineering Mechanics, refType=null, unstructuredReference=YU Xiaohui, LÜ Dagang, FAN Feng. Seismic damage assessment of rc frame structures based on vulnerabilty index[J]. Engineering Mechanics, 2017, 34(1): 69-75, 100. (in Chinese), articleTitle=Seismic damage assessment of rc frame structures based on vulnerabilty index, refAbstract=null), Reference(id=1244335217129931739, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, doi=null, pmid=null, pmcid=null, year=2020, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[28], rfOrder=43, authorNames=乔云龙, journalName=null, refType=null, unstructuredReference=乔云龙. 框架结构地震反应的不确定性分析[D]. 哈尔滨: 中国地震局工程力学研究所, 2020., articleTitle=框架结构地震反应的不确定性分析, refAbstract=null), Reference(id=1244335217192846302, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, doi=null, pmid=null, pmcid=null, year=2020, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[28], rfOrder=44, authorNames=QIAO Yunlong, journalName=null, refType=null, unstructuredReference=QIAO Yunlong. Uncertainty analysis of seismic response of frame structures[D]. Harbin: Institute of Engineering Mechanics, China Earthquake Administration, 2020. (in Chinese), articleTitle=Uncertainty analysis of seismic response of frame structures, refAbstract=null), Reference(id=1244335217285120994, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, doi=null, pmid=null, pmcid=null, year=2009, volume=29, issue=6, pageStart=102, pageEnd=107, url=null, language=null, rfNumber=[29], rfOrder=45, authorNames=刘如山, 胡少卿, 邬玉斌, journalName=地震工程与工程振动, refType=null, unstructuredReference=刘如山, 胡少卿, 邬玉斌, 等. 基于地震动参数的结构易损性表达方法研究[J]. 地震工程与工程振动, 2009, 29(6): 102-107., articleTitle=基于地震动参数的结构易损性表达方法研究, refAbstract=null), Reference(id=1244335217339646950, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, doi=null, pmid=null, pmcid=null, year=2009, volume=29, issue=6, pageStart=102, pageEnd=107, url=null, language=null, rfNumber=[29], rfOrder=46, authorNames=LIU Rushan, HU Shaoqing, WU Yubin, journalName=Earthquake Engineering and Engineering Dynamics, refType=null, unstructuredReference=LIU Rushan, HU Shaoqing, WU Yubin, et al. Research on structure vulnerability expression way based on seismic ground motion parameters[J]. Earthquake Engineering and Engineering Dynamics, 2009, 29(6): 102-107. 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articleId=1244334017403793722, language=EN, label=Fig. 5, caption=Response spectra of the 30 selected ground motion waves, figureFileSmall=Bwq+LDRoDYQ4VnmSacf4mg==, figureFileBig=aex8l2X7dM/mv7TolgAXWA==, tableContent=null), ArticleFig(id=1244335207055213172, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, language=CN, label=图5, caption=30条地震波的反应谱, figureFileSmall=Bwq+LDRoDYQ4VnmSacf4mg==, figureFileBig=aex8l2X7dM/mv7TolgAXWA==, tableContent=null), ArticleFig(id=1244335207160070779, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, language=EN, label=Fig. 6, caption=Damage state distribution for all buildings under different seismic intensities, figureFileSmall=dnXBtMl7eD6mks7JxujKKg==, figureFileBig=QVzkXvKngizOEQAmwzFyjw==, tableContent=null), ArticleFig(id=1244335207260734085, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, language=CN, label=图6, 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figureFileBig=/m3NBwUUmrp+EIik+M6M3Q==, tableContent=null), ArticleFig(id=1244335208074429098, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, language=EN, label=Fig. 10, caption=Beta distributions of building damage index under different seismic intensities, figureFileSmall=I3GBheNaURt9OHaxF/+WCw==, figureFileBig=iL2Zfd0smL18HuEBgtk6nA==, tableContent=null), ArticleFig(id=1244335208162509487, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, language=CN, label=图10, caption=不同烈度下建筑损伤指数的Beta分布模型, figureFileSmall=I3GBheNaURt9OHaxF/+WCw==, figureFileBig=iL2Zfd0smL18HuEBgtk6nA==, tableContent=null), ArticleFig(id=1244335208246395574, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, language=EN, label=Table 1, caption=

Ranges of inter story drift ratio values for structural damage state

, figureFileSmall=null, figureFileBig=null, tableContent=
结构类型几乎完好轻微破坏中等破坏严重破坏倒塌
框架结构[0，1/550）[1/550，1/100）[1/100，1/50）[1/50，1/25）[1/25，1）
砌体结构[0，1/1600）[1/1600，1/700）[1/700，1/350）[1/350，1/200）[1/200，1）
), ArticleFig(id=1244335208527413949, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, language=CN, label=表1, caption=

结构损伤状态层间位移角取值范围

, figureFileSmall=null, figureFileBig=null, tableContent=
结构类型几乎完好轻微破坏中等破坏严重破坏倒塌
框架结构[0，1/550）[1/550，1/100）[1/100，1/50）[1/50，1/25）[1/25，1）
砌体结构[0，1/1600）[1/1600，1/700）[1/700，1/350）[1/350，1/200）[1/200，1）
), ArticleFig(id=1244335209928311491, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, language=EN, label=Table 2, caption=

Specific information of the 30 selected ground motion waves

, figureFileSmall=null, figureFileBig=null, tableContent=
编号RSN地震动文件名震级场地类别PGA/（m/s2）编号RSN地震动文件名震级场地类别PGA/（m/s2）
112RSN12_KERN.PEL_PEL090.AT27.36Ⅱ0.413 816860RSN860_LANDERS_H05000.AT27.28Ⅱ0.797 7
2142RSN142_TABAS_SED-L1.AT27.35Ⅱ0.263 117862RSN862_LANDERS_IND000.AT27.28Ⅱ1.018 2
315RSN15_KERN_TAF021.AT27.36Ⅱ1.557 118863RSN863_LANDERS_ING000.AT27.28Ⅱ0.417 9
4164RSN164_IMPVALL.H_HCPE147.AT26.53Ⅱ1.649 319865RSN865_LANDERS_116000.AT27.28Ⅱ0.414 7
539RSN39_BORREGO_A-PAS180.AT26.63Ⅱ0.069 820867RSN867_LANDERS_FLE144.AT27.28Ⅱ0.428 0
651RSN51_SFERN_PVE065.AT26.61Ⅱ0.252 42186RSN86_SFERN_SON033.AT26.61Ⅱ0.228 2
7582RSN582_SMART1.45_45O08EW.AT27.3Ⅱ1.388 022870RSN870_LANDERS_OBR000.AT27.28Ⅱ0.417 0
8834RSN834_LANDERS_ARC172.AT27.28Ⅱ0.279 523872RSN872_LANDERS_W15090.AT27.28Ⅱ0.254 4
9842RSN842_LANDERS_FLO020.AT27.28Ⅱ0.417 324875RSN875_LANDERS_NYA090.AT27.28Ⅱ0.248 6
10844RSN844_LANDERS_BUE250.AT27.28Ⅱ0.549 825880RSN880_LANDERS_MCF000.AT27.28Ⅱ1.236 8
11845RSN845_LANDERS_VIR200.AT27.28Ⅱ0.276 726881RSN881_LANDERS_MVH045.AT27.28Ⅱ2.185 9
12846RSN846_LANDERS_DEV000.AT27.28Ⅱ0.289 527882RSN882_LANDERS_FHS000.AT27.28Ⅱ1.332 9
13850RSN850_LANDERS_DSP000.AT27.28Ⅱ1.678 028883RSN883_LANDERS_STC090.AT27.28Ⅱ0.348 0
14851RSN851_LANDERS_DWN000.AT27.28Ⅱ0.504 829884RSN884_LANDERS_PSA000.AT27.28Ⅱ0.741 1
1585RSN85_SFERN_SJC033.AT26.61Ⅱ0.424 030886RSN886_LANDERS_PLC000.AT27.28Ⅱ0.455 9
), ArticleFig(id=1244335210041557706, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, language=CN, label=表2, caption=

30条地震波的具体信息

, figureFileSmall=null, figureFileBig=null, tableContent=
编号RSN地震动文件名震级场地类别PGA/（m/s2）编号RSN地震动文件名震级场地类别PGA/（m/s2）
112RSN12_KERN.PEL_PEL090.AT27.36Ⅱ0.413 816860RSN860_LANDERS_H05000.AT27.28Ⅱ0.797 7
2142RSN142_TABAS_SED-L1.AT27.35Ⅱ0.263 117862RSN862_LANDERS_IND000.AT27.28Ⅱ1.018 2
315RSN15_KERN_TAF021.AT27.36Ⅱ1.557 118863RSN863_LANDERS_ING000.AT27.28Ⅱ0.417 9
4164RSN164_IMPVALL.H_HCPE147.AT26.53Ⅱ1.649 319865RSN865_LANDERS_116000.AT27.28Ⅱ0.414 7
539RSN39_BORREGO_A-PAS180.AT26.63Ⅱ0.069 820867RSN867_LANDERS_FLE144.AT27.28Ⅱ0.428 0
651RSN51_SFERN_PVE065.AT26.61Ⅱ0.252 42186RSN86_SFERN_SON033.AT26.61Ⅱ0.228 2
7582RSN582_SMART1.45_45O08EW.AT27.3Ⅱ1.388 022870RSN870_LANDERS_OBR000.AT27.28Ⅱ0.417 0
8834RSN834_LANDERS_ARC172.AT27.28Ⅱ0.279 523872RSN872_LANDERS_W15090.AT27.28Ⅱ0.254 4
9842RSN842_LANDERS_FLO020.AT27.28Ⅱ0.417 324875RSN875_LANDERS_NYA090.AT27.28Ⅱ0.248 6
10844RSN844_LANDERS_BUE250.AT27.28Ⅱ0.549 825880RSN880_LANDERS_MCF000.AT27.28Ⅱ1.236 8
11845RSN845_LANDERS_VIR200.AT27.28Ⅱ0.276 726881RSN881_LANDERS_MVH045.AT27.28Ⅱ2.185 9
12846RSN846_LANDERS_DEV000.AT27.28Ⅱ0.289 527882RSN882_LANDERS_FHS000.AT27.28Ⅱ1.332 9
13850RSN850_LANDERS_DSP000.AT27.28Ⅱ1.678 028883RSN883_LANDERS_STC090.AT27.28Ⅱ0.348 0
14851RSN851_LANDERS_DWN000.AT27.28Ⅱ0.504 829884RSN884_LANDERS_PSA000.AT27.28Ⅱ0.741 1
1585RSN85_SFERN_SJC033.AT26.61Ⅱ0.424 030886RSN886_LANDERS_PLC000.AT27.28Ⅱ0.455 9
), ArticleFig(id=1244335210171581137, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, language=EN, label=Table 3, caption=

Proportion and quantity of damage to regional buildings under different earthquake intensities

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烈度几乎完好轻微中等严重倒塌
6度23（4.76%）460（95.24%）0（0%）0（0%）0（0%）
7度0（0%）390（80.75%）93（19.25%）0（0%）0（0%）
8度0（0%）0（0%）390（80.75%）23（4.76%）70（14.49%）
9度0（0%）0（0%）0（0%）390（80.75%）93（19.25%）
), ArticleFig(id=1244335210263855829, tenantId=1146029695717560320, journalId=1243988319449690156, articleId=1244334017403793722, language=CN, label=表3, caption=

不同地震烈度下区域建筑的损伤数量及损伤比例

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烈度几乎完好轻微中等严重倒塌
6度23（4.76%）460（95.24%）0（0%）0（0%）0（0%）
7度0（0%）390（80.75%）93（19.25%）0（0%）0（0%）
8度0（0%）0（0%）390（80.75%）23（4.76%）70（14.49%）
9度0（0%）0（0%）0（0%）390（80.75%）93（19.25%）
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考虑地震动不确定性的区域建筑震害模拟及损伤概率估计
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滕菲 1 , 王东明 1 , 张耀文 2 , 王方博 2, 3
世界地震工程 | 常规论文 2025,41(4): 145-154
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世界地震工程 | 常规论文 2025, 41(4): 145-154
考虑地震动不确定性的区域建筑震害模拟及损伤概率估计
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滕菲1 , 王东明1 , 张耀文2, 王方博2, 3
作者信息
  • 1.中国地震灾害防御中心，北京　100029
  • 2.天津大学　土木工程系，天津　300350
  • 3.重庆大学　山地城镇建设与新技术教育部重点实验室，重庆　400045

    • 滕菲（1986—），女，高级工程师，硕士，主要从事工程结构抗震研究。E-mail：

通讯作者:

王东明（1977—），男，研究员，博士，主要从事地震灾害风险评估、情景构建及震害仿真、震害预测等方面的研究。E-mail：
Consideration of ground motion uncertainty in regional buildings damage simulation and probabilistic damage estimation
Fei TENG1 , Dongming WANG1 , Yaowen ZHANG2, Fangbo WANG2, 3
Affiliations
  • 1.China Earthquake Disaster Prevention Center, Beijing 100029, China
  • 2.Department of Civil Engineering, Tianjin University, Tianjin 300350, China
  • 3.Key Laboratory of New Technology for Construction of Cities in Mountain Area, Ministry of Education, Chongqing University, Chongqing 400045, China
出版时间: 2025-10-01 doi: 10.19994/j.cnki.WEE.2025.0067
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摘要
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地震动具有较大不确定性，且同一幅值下不同地震动反应谱具有明显差异，对区域建筑震害估计结果影响显著。该研究开发了适用于多层RC框架结构和设防砌体结构的区域建筑震害模拟程序，可以方便快捷地进行设定地震下的区域建筑震害模拟，并基于此开展了考虑地震动不确定性的区域震害模拟和损伤概率估计。选取赤峰市主城区典型区域为研究区域，选择30条实际地震动作为地震动输入以考虑其不确定性，将地震动幅值分别调幅至设定烈度（0.05、0.10、0.20、0.40 g），分别开展单条和多条地震动输入下的区域建筑震害模拟，分析地震动不确定性对区域建筑震害结果的影响。根据设定烈度下的震害结果，建立了基于Beta分布的区域建筑损伤指数概率密度分布模型。研究结果表明：多条地震动输入考虑了地震动的不确定性，能够更加科学、客观地反映区域建筑的震害情况；建立的Beta分布模型，可以用于估计相似区域建筑的震后损伤情况。研究结果可为区域建筑安全评估和抗震设防等提供参考。

地震动不确定性  /  震害模拟  /  区域建筑  /  Beta分布  /  损伤估计

Ground motion has significant uncertainty, and different ground motion response spectra under the same amplitude have significant differences, which have a significant impact on the estimation of seismic damage to regional buildings. This study developed a regional building seismic damage simulation program suitable for multiple-story masonry and concrete frame structures, which can conveniently and quickly simulate regional buildings seismic damage under set earthquakes, and performed regional building damage simulations and probabilistic analysis with motion uncertainties. A typical urban region in Chifeng city was selected as the research area: 30 ground motions were selected to consider their uncertainty, and the ground motions amplitudes were modulated to the set intensity (0.05 g, 0.10 g, 0.20 g, and 0.40 g). Then seismic damage simulation of regional buildings under single and multiple seismic inputs were conducted respectively, the impact of seismic uncertainty on the seismic damage results of regional buildings was analyzed. Based on the seismic damage results under the set intensities, a probability density distribution model of regional buildings damage index based on Beta distribution was established. Results indicate that multiple seismic inputs take into account the uncertainty of seismic motion, which can more scientifically and objectively reflect the seismic damage situation of regional buildings; The established Beta distribution model can be used to estimate the post-earthquake damage of buildings in similar areas. The research results can provide reference for regional buildings safety assessment and seismic fortification.

ground motion uncertainty  /  seismic damage simulation  /  regional buildings  /  Beta distribution  /  damage estimation
滕菲, 王东明, 张耀文, 王方博. 考虑地震动不确定性的区域建筑震害模拟及损伤概率估计. 世界地震工程, 2025 , 41 (4) : 145 -154 . DOI: 10.19994/j.cnki.WEE.2025.0067
Fei TENG, Dongming WANG, Yaowen ZHANG, Fangbo WANG. Consideration of ground motion uncertainty in regional buildings damage simulation and probabilistic damage estimation[J]. World Earthquake Engineering, 2025 , 41 (4) : 145 -154 . DOI: 10.19994/j.cnki.WEE.2025.0067
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0　引言
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地震作为一种自然灾害，给人类带来了严重的生命威胁和财产损失。21世纪以来，全球各国地震频繁，我国也受灾严重。根据中国地震台网的记录，2018—2023年间全世界共发生81次7级以上大地震，680次6级以上强烈地震。仅2023年，我国共发生5级以上地震18次，最大地震为甘肃积石山6.2级地震[1]。历年地震数据表明，中国大陆几乎每年都会发生6级以上地震，且强烈地震是导致建筑损坏甚至倒塌的关键因素之一。
区域建筑震害模拟是在指定地震强度下对建筑群损伤情况的估计，主要包括经验法和分析法。经验法主要基于损伤概率矩阵来表示建筑的易损性，例如基于修正麦卡里烈度的损伤矩阵在过去几十年中已广泛应用于城市区域建筑震害模拟[2-3]。分析法通常通过建立力学模型，分析计算后得到建筑的破坏情况，主要包含静力分析法和时程分析法[4]。著名的多灾害损失估计软件HAZUS就采用了静力分析法，但软件选取单自由度体系模拟建筑结构，难以全面考虑结构的动力特性，时程分析法通过对基本运动方程输入加速度时程，积分求解后得到整个时间历程的地震反应。时程分析法不仅可以更好地模拟建筑结构，而且可以综合考虑地震动振幅、频谱和持时3个要素，过去主要应用在单体建筑的震害分析中。近些年随着计算机性能的提升，许多专家学者开始使用时程分析法进行区域建筑震害模拟。东京大学HORI等[5]开发了integrated earthquake simulation（IES）系统，对日本东京市进行了震害模拟，证明了其方法的可行性，但由于IES只能在超级计算机上运行，因此很难大范围推广。LU等[6]和XIONG等[7]先后提出了多层集中质量剪切模型和高层弯剪耦合模型，将区域震害模拟的适用范围扩展到高层建筑领域。林旭川等[8]开发了城市建筑群地震灾害数值仿真系统YouSimulator，实现了建筑群的震害等级评估，并成功应用到兰州市城关区、云南省漾濞县城等区域的建筑群震害模拟和风险评估中[9-11]。参考单体建筑的精细化模拟，SHEN等[12]提出了纤维梁-分层壳建筑群模型，WEN等[13]利用简单结构信息通过机器学习构建了建筑群OpenSees二维有限元模型。基于多层集中质量剪切模型，本研究开发了一种主要适用于多层砌体和钢筋混凝土框架结构的区域建筑震害模拟程序，每分钟可以输出大约100栋建筑响应结果。程序最大特点是使用方便和计算迅速，应用中具有很好的时效性。
目前有关区域震害模拟的理论研究已经相对完善[14]。但以往有关区域震害模拟的研究通常采用单一地震动输入或者将单一地震动等比例调幅到某一设防烈度进行分析，并没有考虑到相同地震动幅值下反应谱存在不确定性。在实际的区域震害模拟中，建筑结构响应随着地震动的变化而发生变化，有时差异几倍甚至十几倍[15]。本研究利用开发的区域建筑震害模拟程序，基于MDOF剪切层模型和非线性时程分析方法，以赤峰市主城区典型区域为研究对象，选取30条实际地震动作为地震动输入以考虑地震动的不确定性，进行0.05、0.10、0.20、0.40 g多个设防烈度下的结构地震响应分析，并将建筑群震害损伤结果与单一地震动下的震害结果进行对比。最后，采用Beta分布，建立区域建筑损伤指数的概率密度分布模型，用于估计区域建筑震害损伤的程度，可为未来区域建筑的震后损伤指数估计、损伤状态分布统计提供参考。
1　区域建筑震害模拟程序开发
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1.1　震害模拟程序开发框架
震害模拟程序主要适用于多层RC框架结构和设防砌体结构，开发整体流程如图1所示。震害模拟程序分为5个步骤，分别是区域建筑信息获取、建立多自由度剪切层模型、弹塑性时程分析、损伤状态判定和位移响应可视化。具体来说，首先，将地理信息系统的GIS建筑群数据转化为基于物理的建筑结构，并给出建筑群的空间分布；其次，根据已知的物理参数（包括结构高度、结构类型和建造年代等）求解力学参数（包括质量矩阵、刚度矩阵、层屈服承载力和层屈服位移等），建立每个建筑的多自由度剪切层模型；然后，将建筑群模型参数信息和地震动信息输入多自由度非线性时程分析程序，进行建筑群弹塑性时程分析，求解出建筑群地震响应信息（包括位移、速度、加速度）；接着，根据求解的建筑群地震响应信息，进行建筑损伤指数计算和损伤状态判定，并给出区域建筑震害分布图；最后，利用求解的建筑群地震响应信息，导出VTK可视化数据文件，在Paraview中展示建筑群位移响应动画。
该研究采用集中质量法对多层建筑进行简化，建立多自由度集中质量剪切层模型。根据牛顿第二定律，可以得到体系的动力学方程如式（1）所示：
式中：M、K、C分别为建筑质量、刚度、阻尼矩阵；u、、分别代表建筑位移、速度、加速度响应；p（t）代表地震作用。
1.2　层间恢复力模型及结构损伤状态判定
本文采用三折线刚度退化恢复力模型[16-18]来反映结构在弹塑性阶段的层间恢复力与变形关系，其恢复力特性曲线如图2所示。该模型一般由5个参数确定：初始刚度k1、开裂后刚度比α1、屈服后刚度比α2、屈服位移xy，以及开裂位移xc。k1取结构的初始刚度，层间初始刚度由公式（2）计算。
式中：φ1代表结构一阶振型的振型向量；m代表结构单层质量；T1代表结构一阶周期；A代表结构的单层面积；I代表单位矩阵，与结构层数有关。
层间恢复力模型参数取值方面，主要参考陆新征等[14]和XIONG等[19]研究成果，其研究成果具有较为严密的力学基础，且基于大量试验数据统计结果，具有一定的参考价值。值得注意的是，RC框架结构和设防砌体结构的层间恢复力模型参数取值方法相同，主要不同点在于初始刚度和屈服超强系数等取值不同。
但由于Takeda模型需要设置开裂点，且没有下降段，该研究恢复力模型参数的设置与陆新征等[14,19]不完全相同。该研究层间恢复力模型参数取值的主要流程为：①根据底部剪力法计算每层设计承载力，考虑不同结构类型屈服超强系数，计算屈服承载力；②屈服位移xy取规范设计弹性层间位移角与层高之积；③由于Takeda模型需要设置开裂点，该研究取开裂位移xc为屈服位移xy的0.5倍；④根据框架或砌体结构周期估算公式，计算开裂前刚度（初始刚度k1）；⑤根据确定好的开裂点和屈服点，计算开裂后的刚度比α1；⑥屈服后刚度比α2取为0.1。至此，基于Takeda的层间恢复力模型确定完毕。
RC框架结构和砌体结构的损伤状态可以用层间位移角限值来确定。本文综合考虑规范规定及各学者取值建议，确定了框架结构和砌体结构损伤状态层间位移角的取值范围[20-24]，见表1。将结构的损伤状态划分为5个等级，分别为基本完好、轻微破坏、中等破坏、严重破坏和倒塌。
2　区域建筑信息及地震动选取
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2.1　区域建筑信息
城市中多层建筑的数量巨大，一旦发生大面积的破坏将导致非常严重的后果。本文算例选取的研究区域位于赤峰市红山区长青公园地区，属于城市中心城区。该区域东至火花路，西接昭乌达路，北起哈达街，南至钢铁街，东西宽约1.2 km，南北宽约0.8 km，整个研究区域面积约为1.0 km2。目标区域抗震设防烈度为7度，设计基本地震加速度值为0.15 g，设计地震分组为第一组，场地类别为Ⅱ类。
基于GIS数据，可获取该区域内建筑栋数、每栋建筑的层数、建筑角点坐标等基本属性信息。结合风险普查房屋调查工作成果，区域内建筑群主要以多层建筑为主，包括居民住宅、银行、商场、学校等；结构类型主要是RC框架和砌体结构，大部分建筑于2000年以后修建，少量建筑为20世纪80年代和90年代修建。基于以上数据基础，本算例作出如下假定：①由于部分单体建筑详细的结构类型信息缺失，4层及以下建筑结构类型为设防砌体结构，4层以上为RC框架结构；②建造时间均设置为2000年。图3（a）展示了该区域建筑的空间分布，区域内共483栋建筑；结构类型和建筑层数的占比分布如图3（b）和3（c）所示。
2.2　地震动选取
单条地震动的震害模拟选取太平洋地震工程研究中心PEER（Pacific Earthquake Engineering Research Center）地震动数据库中的RSN39地震动记录，记录来自1968年美国加州Borrego山地震中的Pasadena-CIT Athenaeum台站。地震动加速度时程曲线如图4（a）所示，持时60.280 s，时间间隔0.005 s，加速度反应谱如图4（b）所示。
在考虑地震动多样性的震害模拟中，从PEER数据库中挑选了30条地震动作为区域建筑震害分析的样本数据。根据我国《建筑抗震设计规范》（GB 50011—2010）[20]，基本周期考虑前6 s。本文选取的结构位于7度区、Ⅱ类场地，因PEER是使用地下30 m的等效剪切波速VS30作为场地的划分依据，与我国的场地类别划分依据不同，故需要将VS30换算为我国划分场地对应的等效剪切波速[25]，其中我国规范Ⅱ类场地对应的VS30为260~510 m/s。根据ATC-63报告中建议，选择震级大于6.5级，地震动峰值加速度PGA（peak ground acceleration）大于0.2 g，震中距大于10 km的远场地震动记录作为输入样本[26]。表2描述了所选取30条地震动记录的RSN（record sequence number）、地震动分量、震级、场地土类别和PGA信息。尽可能使地震动的频谱信息足够丰富，以此弥补反应谱不确定性给结果带来的差异。将选取的30条地震动记录调幅到0.15 g（研究区域设计基本地震加速度），并与规范设计反应谱进行对比，如图5所示。结果表明，在多层建筑和低层建筑基本周期段（基本周期小于2 s），设计反应谱与选取地震动反应谱吻合较好。但在长周期段，选取的地震波反应谱均值较设计反应谱大，使选取的地震波略为保守。考虑到近年全球大地震产生的地震动均远超预期，选取略保守的地震动反应谱，可以使建筑群震害模拟结果更真实反应未来破坏性大地震的震害。
3　设定烈度下的区域建筑震害模拟结果分析
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3.1　基于单条地震动的震害模拟
本研究中，6、7、8、9度设防地震对应的基本地震动峰值加速度分别取0.05、0.10、0.20、0.40 g。对RSN39地震动的峰值加速度分别调幅至0.05、0.10、0.20、0.40 g，进行不同设防烈度下的区域震害模拟。
图6展示了研究区域建筑物在4个地震烈度下的损伤破坏状态。总体上看，随着地震动强度的增大，区域建筑震害越来越严重。表3详细描述了设定烈度下区域建筑的损伤状态比例及损伤数量分布情况，当输入地震动调幅为0.05 g时，95.24%的建筑为轻微破坏，4.76%的建筑为几乎完好，6度地震对建筑的破坏影响不大；当输入地震动调幅为0.10 g时，80.75%的建筑为轻微破坏，19.25%的建筑为中等破坏，发生中等破坏的建筑中，绝大部分为砌体结构，也说明了砌体结构的抗震能力低于RC框架；7度地震对区域建筑的破坏可控，大部分建筑通过维修仍然可以正常使用；当输入地震动调幅为0.20 g时，统计发现80.75%的建筑为中等破坏，4.76%的建筑为严重破坏，甚至倒塌；当输入地震动调幅至0.40 g时，区域建筑的损伤状态为严重破坏占比提高至80.75%，倒塌的比例为19.25%。8度和9度条件下，倒塌的建筑主要为砌体结构和少量层数较高的框架结构，大多数框架结构破坏严重。总体而言，区域建筑总体损伤情况基本满足“小震不坏，中震可修，大震不倒”的抗震设计目标；分析结果表明，RC框架结构的抗震性能好于砌体结构。
3.2　考虑地震动不确定性的震害模拟
在考虑地震动不确定性的震害模拟中，通过选取的30条地震动记录，对每个地震动调幅至0.05、0.10、0.20、0.40 g，进行设定烈度下的区域建筑震害模拟。分别计算不同烈度下的建筑损伤情况，并进行损伤概率估计。
图7描绘了不同烈度下所有建筑震害模拟损伤柱状图，图中的损伤比例指区域建筑不同损伤状态的百分比。不同烈度下单一地震动和30条地震动损伤比例堆叠图如图8所示，其中30条地震动损伤比例堆叠图是取30条地震动的均值结果。在6度（0.05 g）下，大部分建筑的损伤等级为几乎完好和轻微破坏，几乎完好的比例较单条地震动下的结果有了显著提高，从4.76%增长到28.45%，单条地震动计算和30条地震动计算两种结果都说明6度地震对区域建筑的损伤都集中在几乎完好和轻微破坏这两个状态。在7度（0.10 g）下，几乎所有工况下区域建筑的轻微破坏比例都达到了近70%，只有工况19的损伤情况主要集中在几乎完好和中等破坏，这可能与第19地震动的频谱信息有关。通过图8的对比，能看出7度（0.10 g）下两种计算结果的比例分布基本相差不大。在8度（0.20 g）下，通过图7（c）能够看出30条地震动下区域建筑的损伤情况主要集中在轻微破坏和中等破坏，轻微破坏和中等破坏两个比例之和占73%，单条地震动下中等破坏和轻破坏分别占80.75%和0，两种结果的损伤比例显著不同。在9度（0.40 g）下，从图8可以看出多条地震动下的损伤等级分布更加多样，主要分布在中等破坏、严重破坏和倒塌。综合以上分析，多条地震动输入相比单条地震动输入，可以更加综合、全面地反映不同幅值下地震动对建筑损伤的影响；而单条地震动输入的损伤情况则较为片面、单一。
结构损伤等级划分为5类：几乎完好、轻微破坏、中等破坏、严重破坏和倒塌，分别对应的损伤指数为[0，0.10）、[0.10，0.30）、[0.30，0.55）、[0.55，0.85）和[0.85~1.00）[27]。Beta分布是在[0，1]上的连续型分布，Beta分布关于随机变量x的概率密度函数[28]为
其中，a和b为形状参数且均大于0，Beta函数B（a，b）可表示为
显然，Beta密度分布函数在x∈[0，1]区间内符合全概率分布性质，即：
Beta密度分布函数在x∈[0，1]区间内符合全概率分布的性质，这与给定某烈度下结构各个破坏等级概率分布之和为1具有同样的性质[29]。因此，本研究将不同地震烈度下区域建筑损伤指数来建立Beta分布函数，得到不同损伤指数的概率密度，对区域建筑的震害情况进行更加直观的描述。
设定烈度下，对483栋建筑分别输入30条完成调幅的地震动，共计算14 490次损伤指数。图9展示了各地震烈度下实际概率密度分布与Beta函数拟合曲线，由图可见，用Beta分布来拟合多条地震动下区域建筑的损伤指数分布，能够基本描述不同地震动下区域建筑损伤指数的分布特征。由图9可以看出，在地震烈度较小时（如6度），实际概率密度分布较为集中，主要是由于较小的地震烈度造成的建筑损伤较小，虽然考虑了地震动的不确定性，但是计算的损伤指数均较小，损伤指数分布集中。然而，在9度（0.40 g）下，地震动具有不确定性。不同的地震动频谱对建筑地震响应差异很大（如图5所示），进而造成显著的建筑损伤差异，且9度情况下结构一般均进入非线性，因此损伤指数分布会较为分散。
图10为各地震烈度下建筑损伤指数概率密度分布，对比图7震害模拟柱状图，概率密度分布情况符合预期。通过得到的建筑损伤指数概率密度分布图，可以选择任意的损伤指数区间，计算对应区间的损伤概率，对区域建筑的损伤状态估计和震害评估具有理论意义。
4　结论
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文中考虑地震动的不确定性，进行了赤峰市主城区典型区域建筑震害模拟，主要包括单条地震动震害模拟和30条地震动震害模拟，并且利用30条地震动震害模拟结果建立了区域建筑损伤概率分布模型。研究主要得出以下结论：
1）在考虑地震动不确定性的区域建筑震害模拟中，8度和9度下倒塌率分别为12.40%和27.24%，大震下倒塌率较低，区域建筑总体抗震性能较好。另外，倒塌的建筑中主要为4层以下砌体结构，也说明了砌体结构在抗震方面的劣势。
2）与较单一地震动的区域震害模拟相比，考虑地震动不确定性的区域建筑震害模拟能够比较科学、客观地反映区域建筑未来可能遇到的损伤情况，可为区域建筑的震害评估、抗震设防等提供参考。
3）研究建立了区域建筑损伤指数的Beta概率密度分布模型。研究发现，以区域建筑的损伤指数为基础，建立基于Beta分布的区域建筑损伤指数概率密度分布模型，不同设定烈度下拟合的Beta概率密度曲线与实际的损伤指数分布图吻合较好。建立的Beta分布模型可为设定烈度下相似区域建筑的震后损伤估计提供参考。
基金
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  • 国家自然科学基金项目(52278541)
  • 国家重点研发计划重大自然灾害防控与公共安全专项(2022VEC3006404)
  • 山地城镇建设与新技术教育部重点实验室开放基金(LNTCCMA-20220111)
文献
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2025年第41卷第4期
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文章信息
doi: 10.19994/j.cnki.WEE.2025.0067
  • 接收时间：2024-10-20
  • 首发时间：2026-03-27
  • 出版时间：2025-10-01
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  • 收稿日期：2024-10-20
  • 修回日期：2025-01-13
基金
国家自然科学基金项目(52278541)
国家重点研发计划重大自然灾害防控与公共安全专项(2022VEC3006404)
山地城镇建设与新技术教育部重点实验室开放基金(LNTCCMA-20220111)
作者信息
    1.中国地震灾害防御中心，北京　100029
    2.天津大学　土木工程系，天津　300350
    3.重庆大学　山地城镇建设与新技术教育部重点实验室，重庆　400045

通讯作者:

王东明（1977—），男，研究员，博士，主要从事地震灾害风险评估、情景构建及震害仿真、震害预测等方面的研究。E-mail：
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https://castjournals.cast.org.cn/joweb/sjdzgc/CN/10.19994/j.cnki.WEE.2025.0067
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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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