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Article(id=1241794075444187275, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241794070289387562, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2025.0511, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1712073600000, receivedDateStr=2024-04-03, revisedDate=1733673600000, revisedDateStr=2024-12-09, acceptedDate=null, acceptedDateStr=null, onlineDate=1773996379004, onlineDateStr=2026-03-20, pubDate=1761062400000, pubDateStr=2025-10-22, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773996379004, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773996379004, creator=13701087609, updateTime=1773996379004, 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=110, endPage=120, ext={EN=ArticleExt(id=1241794075733594264, articleId=1241794075444187275, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Study on the influence of ground motion duration on the damage spectra of single-degree-of-freedom systems, columnId=1241794071602200899, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

The duration of ground motion can significantly influence the cumulative damage and failure levels of structures, but its impact on structural response is inadequately considered in current seismic design. To explore the effect of ground motion duration on structural damage, this study employs a spectral matching method combined with wavelet transform to select 115 ground motion records of varying durations from the Japan strong-motion database (K-NET). Earthquake damage spectra under two different restoring force models were calculated, and a comprehensive analysis was conducted on the effects of ground motion duration, yield strength reduction factor, structural natural period and other factors on the structural damage spectrum. Additionally, 585 natural earthquake records of varying durations and different site conditions were selected from the Pacific Earthquake Engineering Research Center (PEER) database. Taking into account the combined influences of ground motion duration, yield strength reduction factor, structural restoring force model, and site conditions, a damage spectrum prediction model was developed using a differential evolution algorithm. Compared with existing prediction models, the proposed model reduces relative errors by more than 40%, which offers improved accuracy for predicting damage spectra that consider the effect of duration. The results of this study provide valuable insights for structural seismic design and damage assessment when considering the impact of ground motion duration.

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地震动持时会显著影响结构累积损伤和破坏水平,但目前抗震设计中,对地震动持时对结构响应的影响考虑不足。为研究地震动持时对结构损伤的影响,文中采用谱匹配并结合小波变换方法,从日本强震动数据库（K-NET）中匹配得到115条不同持时的地震动记录,计算了2种恢复力模型下的地震动损伤谱,并综合分析了地震动持时、屈服强度折减系数和结构自振周期等因素对结构损伤谱的影响。然后,该文从美国太平洋地震工程研究中心（Pacific Earthquake Engineering Research Center, PEER）选取了585条不同场地条件、具有不同持时的天然地震动记录,综合考虑地震动持时、屈服强度折减系数、结构恢复力模型以及场地条件影响,采用差分进化算法建立了损伤谱预测模型计算公式。与已有预测模型的对比研究表明,文中模型相对误差降低了40%以上,能够更好地预测考虑持时的地震动损伤谱,且具有更高精度。研究结果可为考虑地震动持时效应的结构抗震设计和损伤评估等提供参考。

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公茂盛（1976—）,男,研究员,博士,主要从事地震工程研究。E-mail：
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杨郁昂（1999—）,男,硕士研究生,主要从事地震工程研究。E-mail：

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杨郁昂（1999—）,男,硕士研究生,主要从事地震工程研究。E-mail：

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杨郁昂（1999—）,男,硕士研究生,主要从事地震工程研究。E-mail：

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(in Chinese), articleTitle=Effect of earthquake duration on seismic response of structures, refAbstract=null), Reference(id=1241802956136321662, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, doi=null, pmid=null, pmcid=null, year=2021, volume=43, issue=6, pageStart=1436, pageEnd=1443, url=null, language=null, rfNumber=[29], rfOrder=37, authorNames=侯红梅, 刘文锋, 张怀超, journalName=地震工程学报, refType=null, unstructuredReference=侯红梅，刘文锋，张怀超．基于SDOF体系和高层结构的地震动强度指标研究[J]．地震工程学报, 2021, 43(6): 1436-1443., articleTitle=基于SDOF体系和高层结构的地震动强度指标研究, refAbstract=null), Reference(id=1241802956299899526, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, doi=null, pmid=null, pmcid=null, year=2021, volume=43, issue=6, pageStart=1436, pageEnd=1443, url=null, language=null, rfNumber=[29], rfOrder=38, authorNames=HOU Hongmei, LIU Wenfeng, ZHANG Huaichao, journalName=China Earthquake Engineering Journal, refType=null, unstructuredReference=HOU Hongmei, LIU Wenfeng, ZHANG Huaichao. 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figureFileBig=mA6xa4odRtNAMtqkbAkQ+g==, tableContent=null), ArticleFig(id=1241802944694260496, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Fig. 2, caption=Matched to obtain the duration distribution, acceleration spectra, displacement spectra of the ground motion records and the influence of wavelet transform on the duration, figureFileSmall=WUJj1KP1zNkVY09dilwTMQ==, figureFileBig=4AsI65UckRhpY4etgi04Qg==, tableContent=null), ArticleFig(id=1241802944841061148, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=图2, caption=匹配得到地震动记录的持时分布、加速度谱、位移谱以及小波变换对持时的影响, figureFileSmall=WUJj1KP1zNkVY09dilwTMQ==, figureFileBig=4AsI65UckRhpY4etgi04Qg==, tableContent=null), ArticleFig(id=1241802944992056111, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Fig. 3, caption=Hysteresis curves of the model, figureFileSmall=n1Vurr0E6LcHqW1da1T6PA==, figureFileBig=wqx2wcDEcWXToEbzZqE5cA==, tableContent=null), ArticleFig(id=1241802945138856765, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=图3, caption=模型滞回曲线, figureFileSmall=n1Vurr0E6LcHqW1da1T6PA==, figureFileBig=wqx2wcDEcWXToEbzZqE5cA==, tableContent=null), ArticleFig(id=1241802945285657421, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Fig. 4, caption=Relationship between structural damage and ground motion duration when T is 0.2,1.0,3.0 s, figureFileSmall=cUJpv1cDZDVdY97V98IZoA==, figureFileBig=b/rSRcr35bGSd1RWt8a7lw==, tableContent=null), ArticleFig(id=1241802945398903644, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=图4, caption= T为0.2、1.0、3.0 s时结构损伤与地震动持时的关系, figureFileSmall=cUJpv1cDZDVdY97V98IZoA==, figureFileBig=b/rSRcr35bGSd1RWt8a7lw==, tableContent=null), ArticleFig(id=1241802945545704298, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Fig. 5, caption=Pearson correlation coefficient graph, figureFileSmall=nGO+XOqpmsGFp8xjpFYiRQ==, figureFileBig=u1AyXedcsM636c4YkJaLGA==, tableContent=null), ArticleFig(id=1241802945679922044, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=图5, caption=Pearson相关系数图, figureFileSmall=nGO+XOqpmsGFp8xjpFYiRQ==, figureFileBig=u1AyXedcsM636c4YkJaLGA==, tableContent=null), ArticleFig(id=1241802945822528392, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Fig. 6, caption=Damage spectra and damage ratio spectra, figureFileSmall=mhwIVYWC5jjQWnj954MMZw==, figureFileBig=lvMuRUk2Lm0jAa7EzoLrVw==, tableContent=null), ArticleFig(id=1241802946019660695, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=图6, caption=损伤谱与损伤比谱, figureFileSmall=mhwIVYWC5jjQWnj954MMZw==, figureFileBig=lvMuRUk2Lm0jAa7EzoLrVw==, tableContent=null), ArticleFig(id=1241802946275513261, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Fig. 7, caption=Damage spectra under different strength reduction factors for Ds5-95 in the range [40, 60)s, figureFileSmall=iP50UoTkHHtcxQKk70HcHg==, figureFileBig=du16IkdTEc38/9ofkGYo1Q==, tableContent=null), ArticleFig(id=1241802946409731001, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=图7, caption= Ds5-95在[40,60)s之间时不同屈服强度折减系数下的损伤谱, figureFileSmall=iP50UoTkHHtcxQKk70HcHg==, figureFileBig=du16IkdTEc38/9ofkGYo1Q==, tableContent=null), ArticleFig(id=1241802946522977226, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Fig. 8, caption=Damage ratios spectra under different yield strength reduction factors, figureFileSmall=TvNDGBrDdcQeUk1O6+Q63w==, figureFileBig=jie+NwQnpRH4Ydz8zBaifw==, tableContent=null), ArticleFig(id=1241802946665583578, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=图8, caption=不同屈服强度折减系数下的损伤比谱, figureFileSmall=TvNDGBrDdcQeUk1O6+Q63w==, figureFileBig=jie+NwQnpRH4Ydz8zBaifw==, tableContent=null), ArticleFig(id=1241802946799801318, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Fig. 9, caption=Number of natural ground motions at each site, figureFileSmall=1OPzxJ4t13C8MutV8MvC/w==, figureFileBig=6il/2BIwqxAELKu+WGPurg==, tableContent=null), ArticleFig(id=1241802946938213368, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=图9, caption=各场地天然地震动数量, figureFileSmall=1OPzxJ4t13C8MutV8MvC/w==, figureFileBig=6il/2BIwqxAELKu+WGPurg==, tableContent=null), ArticleFig(id=1241802947043069956, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Fig. 10, caption=Regression effects of two hysteretic models, figureFileSmall=kHyBukvgcF1deIHWWDf1ng==, figureFileBig=H66EWtspOFbpdUxMhDdTMQ==, tableContent=null), ArticleFig(id=1241802948536242186, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=图10, caption=2种滞回模型的回归效果, figureFileSmall=kHyBukvgcF1deIHWWDf1ng==, figureFileBig=H66EWtspOFbpdUxMhDdTMQ==, tableContent=null), ArticleFig(id=1241802948687237145, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Fig. 11, caption=Comparison of prediction effects, figureFileSmall=9XnMhbjYG4CZsFvewwaYDA==, figureFileBig=TZNK811AIoDNy9d6eYZwVw==, tableContent=null), ArticleFig(id=1241802948796289060, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=图11, caption=预测效果对比, figureFileSmall=9XnMhbjYG4CZsFvewwaYDA==, figureFileBig=TZNK811AIoDNy9d6eYZwVw==, tableContent=null), ArticleFig(id=1241802948947284018, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Table 1, caption=

Comparison of spectral characteristics of ground motion time histories before and after spectra matching

, figureFileSmall=null, figureFileBig=null, tableContent=
统计参数原始地震动记录统计参数谱匹配后地震动记录
Tm Tmh Tc To Hcov Tm Tmh Tc To Hcov
均值0.6580.4040.6010.4112.559均值0.6520.4210.6450.3672.392
标准差0.1760.1320.1610.1290.581标准差0.1130.1090.1020.0190.482
变异系数0.2680.3280.2680.3140.227变异系数0.1730.2580.1580.0540.201
), ArticleFig(id=1241802949106667584, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=表1, caption=

谱匹配前后地震动时程频谱特征参数对比

, figureFileSmall=null, figureFileBig=null, tableContent=
统计参数原始地震动记录统计参数谱匹配后地震动记录
Tm Tmh Tc To Hcov Tm Tmh Tc To Hcov
均值0.6580.4040.6010.4112.559均值0.6520.4210.6450.3672.392
标准差0.1760.1320.1610.1290.581标准差0.1130.1090.1020.0190.482
变异系数0.2680.3280.2680.3140.227变异系数0.1730.2580.1580.0540.201
), ArticleFig(id=1241802949219913804, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Table 2, caption=

Regression parameters and goodness-of-fit values

, figureFileSmall=null, figureFileBig=null, tableContent=
滞回模型场地类别拟合参数拟合优度
a b c d e
EPPⅠ0-3.7021.3290.1140.8530.0060.932
Ⅰ1-3.5971.2280.1570.8240.0080.912
Ⅱ-3.4881.1530.1170.8450.0010.808
Ⅲ-3.2421.4610.0710.8190.0010.772
Ⅳ-3.6371.2430.1280.8310.0040.935
MCⅠ0-3.5301.1510.1950.8030.0040.916
Ⅰ1-3.8551.2370.1650.8260.0060.932
Ⅱ-3.9050.9240.4110.7840.0070.930
Ⅲ-4.2950.9120.5520.8140.0100.939
Ⅳ-4.5770.7230.9950.7570.0120.948
), ArticleFig(id=1241802949354131540, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=表2, caption=

回归参数及拟合优度值

, figureFileSmall=null, figureFileBig=null, tableContent=
滞回模型场地类别拟合参数拟合优度
a b c d e
EPPⅠ0-3.7021.3290.1140.8530.0060.932
Ⅰ1-3.5971.2280.1570.8240.0080.912
Ⅱ-3.4881.1530.1170.8450.0010.808
Ⅲ-3.2421.4610.0710.8190.0010.772
Ⅳ-3.6371.2430.1280.8310.0040.935
MCⅠ0-3.5301.1510.1950.8030.0040.916
Ⅰ1-3.8551.2370.1650.8260.0060.932
Ⅱ-3.9050.9240.4110.7840.0070.930
Ⅲ-4.2950.9120.5520.8140.0100.939
Ⅳ-4.5770.7230.9950.7570.0120.948
), ArticleFig(id=1241802949467377757, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=EN, label=Table 3, caption=

Natural ground motion records selected for comparing the prediction formulas

, figureFileSmall=null, figureFileBig=null, tableContent=
文件名地震台站 MW VS30 Ds5-95年份
RSN1799_HECTOR_OBR090.AT2Hector MineLA-Obregon Park7.1349.4344.2351999
RSN1823_HECTOR_SAC090.AT2Hector MineSalton City7.1324.5052.4201999
RSN2520_CHICHI.03_HWA013N.AT2Chi-ChiHWA0136.2330.5539.0351999
RSN2548_CHICHI.03_HWA048N.AT2Chi-ChiHWA0486.2345.8928.4121999
RSN2548_CHICHI.03_HWA048W.AT2Chi-ChiHWA0486.2345.8935.8441999
RSN2550_CHICHI.03_HWA050N.AT2Chi-ChiHWA0506.2313.9019.4921999
RSN2550_CHICHI.03_HWA050W.AT2Chi-ChiHWA0506.2313.9018.5921999
RSN2638_CHICHI.03_TCU098E.AT2Chi-ChiTCU0986.2346.5623.2701999
RSN2700_CHICHI.04_CHY025E.AT2Chi-ChiCHY0256.2277.5020.7551999
RSN2744_CHICHI.04_CHY088E.AT2Chi-ChiCHY0886.2318.5220.5301999
RSN2749_CHICHI.04_CHY096W.AT2Chi-ChiCHY0966.2293.6141.6041999
RSN2764_CHICHI.04_HWA011N.AT2Chi-ChiHWA0116.2355.7630.2151999
RSN3320_CHICHI.06_CHY111W.AT2Chi-ChiCHY1116.3276.3477.9401999
RSN3818_HECTOR_RLD360.AT2Hector MineRiverside-Limonite & Downey7.1329.8425.8301999
RSN4925_CHUETSU_AKTH03EW.AT2Chuetsu-okiAKTH036.8320.2377.2202007
RSN5066_CHUETSU_GNM007EW.AT2Chuetsu-okiGNM0076.8287.3745.8102007
RSN5069_CHUETSU_GNM010EW.AT2Chuetsu-okiGNM0106.8297.1994.2402007
RSN51_SFERN_PVE155.AT2San Fernando2516 Via Tejon PV6.6280.5654.2151971
RSN5297_CHUETSU_SIT005EW.AT2Chuetsu-okiSIT0056.8274.7755.0502007
RSN5449_CHUETSU_YMTH08NS.AT2Chuetsu-okiYMTH086.8320.3187.2902007
RSN5463_IWATE_AKT008EW.AT2IwateAKT0086.9298.5076.4102008
RSN5481_IWATE_AKTH03NS.AT2IwateAKTH036.9320.2341.6602008
RSN5488_IWATE_AKTH10NS.AT2IwateAKTH106.9333.5551.3802008
RSN5493_IWATE_AKTH17NS.AT2IwateAKTH176.9288.8245.8902008
RSN5499_IWATE_AOM004NS.AT2IwateAOM0046.9337.1739.3402008
RSN5500_IWATE_AOM005EW.AT2IwateAOM0056.9287.5987.1702008
RSN5573_IWATE_FKSH03NS.AT2IwateFKSH036.9349.7471.0502008
RSN5751_IWATE_YMT008EW.AT2IwateYMT0086.9339.9254.3902008
RSN5767_IWATE_YMTH08EW.AT2IwateYMTH086.9320.3132.3002008
RSN5771_IWATE_YMTH14EW.AT2IwateYMTH146.9310.8855.9402008
RSN5774_IWATE_54008EW.AT2IwateNakashinden Town6.9276.3025.2302008
RSN5836_SIERRA.MEX_EMO270.AT2El Mayor-CucapahEl Centro-Meloland Geot.Array7.2264.5724.6452010
RSN5954_SIERRA.MEX_23631-H1.AT2El Mayor-CucapahSan Bernardino-I10/215 Int7.2271.0033.5652010
RSN6013_SIERRA.MEX_2027B360.AT2El Mayor-CucapahEl Centro-Meadows Union School7.2276.2537.8102010
RSN6014_SIERRA.MEX_0526C090.AT2El Mayor-CucapahMecca Fire Station7.2298.7152.5602010
RSN6572_NIIGATA_GNM012NS.AT2NiigataGNM0126.6358.5338.1002004
RSN6588_NIIGATA_IBR009EW.AT2NiigataIBR0096.6298.2084.1202004
RSN6596_NIIGATA_IBR018NS.AT2NiigataIBR0186.6285.0056.7002004
RSN6643_NIIGATA_KNG006EW.AT2NiigataKNG0066.6330.7183.7102004
RSN6795_NIIGATA_TKY004NS.AT2NiigataTKY0046.6302.2649.4202004
RSN6798_NIIGATA_TKY007NS.AT2NiigataTKY0076.6261.6572.8402004
RSN6818_NIIGATA_TYM007NS.AT2NiigataTYM0076.6328.8141.3502004
RSN6896_DARFIELD_DORCN20W.AT2DarfieldDORC7.0280.2627.9252010
RSN6910_DARFIELD_HMCSN53W.AT2DarfieldHMCS7.0289.6940.5802010
RSN6933_DARFIELD_MAYCN76W.AT2DarfieldMAYC7.0342.7025.5402010
RSN800_LOMAP_SJW160.AT2Loma PrietaSalinas-John & Work6.9279.5621.4951989
RSN8057_CCHURCH_AMBCN86E.AT2ChristchurchAMBC6.2336.9843.6002011
RSN8057_CCHURCH_AMBCS04E.AT2ChristchurchAMBC6.2336.9842.9352011
RSN8127_CCHURCH_SBRCS31E.AT2ChristchurchSBRC6.2263.2013.0602011
RSN869_LANDERS_WST270.AT2LandersLA-N Westmoreland7.3315.0624.0451992
RSN880_LANDERS_MCF090.AT2LandersMission Creek Fault7.2355.4240.7751992
RSN970_NORTHR_FAI095.AT2Northridge-01El Monte-Fairview Av6.7290.6320.1301994
), ArticleFig(id=1241802949593206891, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794075444187275, language=CN, label=表3, caption=

对比预测公式时选取的天然地震动记录

, figureFileSmall=null, figureFileBig=null, tableContent=
文件名地震台站 MW VS30 Ds5-95年份
RSN1799_HECTOR_OBR090.AT2Hector MineLA-Obregon Park7.1349.4344.2351999
RSN1823_HECTOR_SAC090.AT2Hector MineSalton City7.1324.5052.4201999
RSN2520_CHICHI.03_HWA013N.AT2Chi-ChiHWA0136.2330.5539.0351999
RSN2548_CHICHI.03_HWA048N.AT2Chi-ChiHWA0486.2345.8928.4121999
RSN2548_CHICHI.03_HWA048W.AT2Chi-ChiHWA0486.2345.8935.8441999
RSN2550_CHICHI.03_HWA050N.AT2Chi-ChiHWA0506.2313.9019.4921999
RSN2550_CHICHI.03_HWA050W.AT2Chi-ChiHWA0506.2313.9018.5921999
RSN2638_CHICHI.03_TCU098E.AT2Chi-ChiTCU0986.2346.5623.2701999
RSN2700_CHICHI.04_CHY025E.AT2Chi-ChiCHY0256.2277.5020.7551999
RSN2744_CHICHI.04_CHY088E.AT2Chi-ChiCHY0886.2318.5220.5301999
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地震动持时对单自由度体系损伤谱影响研究
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杨郁昂 1, 2 , 公茂盛 1, 2 , 左占宣 1, 2
地震工程与工程振动 | 研究论文 2025,45(5): 110-120
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地震工程与工程振动 | 研究论文 2025, 45(5): 110-120
地震动持时对单自由度体系损伤谱影响研究
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杨郁昂1, 2 , 公茂盛1, 2 , 左占宣1, 2
作者信息
  • 1.中国地震局工程力学研究所地震工程与工程振动重点实验室,黑龙江哈尔滨150080
  • 2.地震灾害防治应急管理部重点实验室,黑龙江哈尔滨150080

    • 杨郁昂（1999—）,男,硕士研究生,主要从事地震工程研究。E-mail：

通讯作者:

公茂盛（1976—）,男,研究员,博士,主要从事地震工程研究。E-mail：
Study on the influence of ground motion duration on the damage spectra of single-degree-of-freedom systems
Yuang YANG1, 2 , Maosheng GONG1, 2 , Zhanxuan ZUO1, 2
Affiliations
  • 1.Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
  • 2.Key Laboratory of Earthquake Disaster Mitigation, Ministry of Emergency Management, Harbin 150080, China
出版时间: 2025-10-22 doi: 10.13197/j.eeed.2025.0511
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摘要
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地震动持时会显著影响结构累积损伤和破坏水平,但目前抗震设计中,对地震动持时对结构响应的影响考虑不足。为研究地震动持时对结构损伤的影响,文中采用谱匹配并结合小波变换方法,从日本强震动数据库（K-NET）中匹配得到115条不同持时的地震动记录,计算了2种恢复力模型下的地震动损伤谱,并综合分析了地震动持时、屈服强度折减系数和结构自振周期等因素对结构损伤谱的影响。然后,该文从美国太平洋地震工程研究中心（Pacific Earthquake Engineering Research Center, PEER）选取了585条不同场地条件、具有不同持时的天然地震动记录,综合考虑地震动持时、屈服强度折减系数、结构恢复力模型以及场地条件影响,采用差分进化算法建立了损伤谱预测模型计算公式。与已有预测模型的对比研究表明,文中模型相对误差降低了40%以上,能够更好地预测考虑持时的地震动损伤谱,且具有更高精度。研究结果可为考虑地震动持时效应的结构抗震设计和损伤评估等提供参考。

地震动持时  /  损伤指数谱  /  屈服强度折减系数  /  单自由度体系

The duration of ground motion can significantly influence the cumulative damage and failure levels of structures, but its impact on structural response is inadequately considered in current seismic design. To explore the effect of ground motion duration on structural damage, this study employs a spectral matching method combined with wavelet transform to select 115 ground motion records of varying durations from the Japan strong-motion database (K-NET). Earthquake damage spectra under two different restoring force models were calculated, and a comprehensive analysis was conducted on the effects of ground motion duration, yield strength reduction factor, structural natural period and other factors on the structural damage spectrum. Additionally, 585 natural earthquake records of varying durations and different site conditions were selected from the Pacific Earthquake Engineering Research Center (PEER) database. Taking into account the combined influences of ground motion duration, yield strength reduction factor, structural restoring force model, and site conditions, a damage spectrum prediction model was developed using a differential evolution algorithm. Compared with existing prediction models, the proposed model reduces relative errors by more than 40%, which offers improved accuracy for predicting damage spectra that consider the effect of duration. The results of this study provide valuable insights for structural seismic design and damage assessment when considering the impact of ground motion duration.

ground motion duration  /  damage index spectrum  /  yield strength reduction factor  /  single-degree-of-freedom system
杨郁昂, 公茂盛, 左占宣. 地震动持时对单自由度体系损伤谱影响研究. 地震工程与工程振动, 2025 , 45 (5) : 110 -120 . DOI: 10.13197/j.eeed.2025.0511
Yuang YANG, Maosheng GONG, Zhanxuan ZUO. Study on the influence of ground motion duration on the damage spectra of single-degree-of-freedom systems[J]. Earthquake Engineering and Engineering Dynamics, 2025 , 45 (5) : 110 -120 . DOI: 10.13197/j.eeed.2025.0511
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0　引言
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近年来,多次大地震造成了巨大的经济损失和人员伤亡。除震级大、震动强外,地震动持时长也是一个重要原因。例如,2008年我国汶川地震中,卧龙强震台地震动总持时长达180 s；2011年日本“3•11”大地震中,地震动总持时长达300 s。目前,有关地震动持时对结构损伤影响的研究尚不充分,研究结果尚未纳入抗震设计规范。特别是用于确定地震荷载的抗震设计谱无法充分反映地震动持时对结构抗震性能的影响[1]。
为了更好地考虑地震动持时进而对结构进行抗震设计,大量研究者开展了关于地震动持时对结构响应影响的分析。结果显示,考虑了累积损伤的指标,如滞回耗能[2]、Park-Ang损伤指数[3]等,与地震动持时相关性较高[4-5],而基于峰值响应的损伤指标,如层间位移角、延性系数等,在结构非线性程度不强时通常与地震动持时相关性不高[6],但当结构非线性程度较高且引起刚度和强度退化时[7-8],基于峰值响应的损伤指标与地震动持时相关性亦较高,因此,需要选择合理的指标和方法将地震动持时的影响纳入抗震设计中,其中一种方法是使用考虑累积损伤的非弹性反应谱。BOZORGNIA等[9]通过归一化滞回耗能和延性需求提出了损伤谱,并指出损伤谱会受到地震动持时的影响；COSENZ等[10]提出了一种包含累积损伤效应的简单方法,并引入了包含等效损伤因子的非弹性谱以考虑地震造成的潜在损伤；ZHAI等[11]提出了一个预测模型来估计主余震型地震的损伤谱,考虑了结构自振周期、强度折减系数、阻尼比、屈服后刚度和场地的影响；SAMANTA等[12]讨论了地震动持时对峰值响应、结构性能和非弹性反应谱的影响,并估计了不同持时下特定周期的结构损伤；WEN等[13]提出了基于全球主余震的损伤谱预测模型,考虑了屈服强度折减系数、结构恢复力模型以及主余震强度之比；杨铭[14]、MOLAZADEH等[15]分别就中美抗震设计谱提出了长短持时下标准滞回耗能谱和延性需求谱的预测模型,考虑了结构自振周期、屈服强度折减系数和结构恢复力模型,并可通过这种方式计算对应的损伤谱；GHAREHBAGHI等[16]使用神经网络和多因素符号回归方法,提出了各场地下平均损伤谱的预测模型,考虑了结构自振周期、硬化比、阻尼比、屈服强度折减系数和Park-Ang损伤指数的参数。综上,非弹性损伤谱相关研究已较为成熟,诸多参数已被纳入预测模型中,但大多研究在考虑地震动持时时仅能给出长短2组地震动的估计值,而无法准确估计特定持时下的损伤谱,预测结果依赖于所选地震动记录的持时分布,若地震动的持时与长短持时组的中位持时差异较大,预测误差可能较大[17]。因此,进一步研究不同地震动持时下的非弹性损伤谱是有必要的。
本文以中国抗震设计谱作为目标谱,采用谱匹配及小波变换方法,从K-NET（kyoshin net）地震动数据库选择并匹配了115条地震动记录,以此为输入开展了不同周期单自由度体系地震反应分析,得到了不同持时地震动的等强度损伤谱及其比谱,并以20 s为区间进行分组和统计分析,分别考虑各组的平均损伤谱和平均持时,分析了地震动持时和损伤谱的关系。然后,选取585条天然地震动并计算得到了损伤谱,然后对不同场地下损伤谱与地震动持时和屈服强度折减系数的关系进行了回归分析,建立了损伤指数谱与地震动持时的关系模型,可用以估计不同持时地震动下的结构损伤。
1　地震动记录选取与匹配
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1.1　地震动持时定义
在进行地震动选取和匹配前,首先需要确定地震动持时定义。从20世纪60年代至今,研究者已经提出了30余种不同的持时定义,这些定义被BOMMER等[18]归类为四大类：括号持时,一致持时、显著持时和有效持时。其中显著持时因为与结构响应相关性较强而被广泛使用[19-20],本文在分析地震动损伤谱时,也采用了显著持时。显著持时定义为占Arias强度一定比例的时间间隔, Arias强度计算公式如式（1）所示：
式中：a（t）为加速度时程；tmax为地震动记录的总时长；g为重力加速度。该持时定义根据5%~75%或95%占比的不同分为70%显著持时（Ds5-75）和90%显著持时（Ds5-95）,相比于其他持时定义,该定义相对稳定,不会因为阈值选择不同导致持时不同,可以代表地震动的强震动段,并在一定程度上反映了地震动的能量特性。文献[4,21]研究表明,90%显著持时Ds5-95与结构反应相关性较高,因此本文在分析时选用Ds5-95作为持时定义,其计算方式见图1。
1.2　地震动的选取与处理
为了研究地震动持时对结构损伤的影响,本文以GB 50011—2010《建筑抗震设计规范》[22]中的抗震设计谱（8度设防,罕遇地震,Ⅱ类场地,设计地震分组为第2组）作为目标谱,根据以下原则从日本K-NET地震动数据库中选取了115条持时不同的地震动记录作为输入。
1）震中距大于20 km且小于200 km。
2）震级大于5级。
3）场地剪切波速VS30在260~510 m/s之间,对应我国抗震规范中的Ⅱ类场地[23]。
由于地震动幅值和频谱特性会显著地影响到结构的损伤和动力响应[24],因此本文使用小波变换方法对选取的地震动记录进行二次处理和匹配。根据文献[25],基于小波变换的谱匹配方法能够保留原始地震动的特征,同时消除地震动幅值和频谱特性差异带来的变异性。为保证匹配效果,本文使用HANCOCK等[25]提出的谱失配概念对匹配效果进行监督,其中谱失配分为平均谱失配δave和最大谱失配δmax,δave检验谱匹配的整体效果,δmax检验谱匹配的局部效果,其计算方法分别如式（2）、式（3）所示：
式中：Sa为匹配后地震动记录的谱加速度；Sat为目标谱的谱加速度；NT为周期点的数量。在匹配过程中,参考文献[15]的研究,分别将δave和δmax控制在5%以及15%以内,以确保匹配效果。
为了检查谱匹配前后地震动时程的频谱特征变化,计算了谱匹配前后所有地震动时程Fourier幅值谱平均周期Tm, Hilbert边际谱平均周期Tmh,加速度反应谱特征周期Tc,平滑化加速度反应谱卓越周期To,以及瞬时频率变异系数Hcov[26],其均值、标准差和变异系数见表1。从各项均值可以看出,谱匹配不会大幅改变地震动时程的频谱特征和非平稳特征,但谱匹配后各频谱特征的标准差和变异系数明显降低,这说明谱匹配会降低地震动时程之间的频谱差异,有效地减小计算时的离散性。图2（a）、（b）、（c）、（d）分别展示了所选地震动的Ds5-95分布、小波变换后的加速度谱、位移谱以及小波变换前后的Ds5-95,可以看出谱匹配效果良好,并保留了地震动时程的持时特征。
2　恢复力模型与损伤指数谱
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本文使用等强度损伤指数谱研究地震动持时的影响[27],损伤指数选用Park-Ang损伤指数。屈服强度折减系数的定义如式（4）所示：
式中：Fe为单自由度系统在地震动作用下保持弹性反应的强度需求；Fy为单自由度系统的屈服强度。
Park-Ang损伤数Id定义如式（5）所示[2]：
式中：μ为延性需求；μu为结构在单调荷载作用下的极限延性能力,根据文献[13]本文取10；EH为结构的滞回耗能需求；xy为屈服位移；β为衡量结构滞回耗能对结构损伤影响的无量纲参数,根据文献[13]本文将β取为0.15。针对不同周期单自由度体系,分别计算后可以得到损伤指数谱。
在进行单自由度体系时程反应分析时,本文选用了理想弹塑性（elastic perfectly plastic, EPP）模型和修正克拉夫（modified Clough, MC）模型这2种恢复力模型,并取MC模型的屈服后刚度为初始刚度的2%[28],这2种恢复力模型滞回曲线见图3。其中EPP模型无结构退化行为,并可代表钢框架结构的恢复力特性, MC模型考虑了再加载路径的刚度退化,并可用于模拟钢筋混凝土结构的弯曲行为,二者在结构模拟和抗震设计上均有广泛应用。
3　损伤指数谱分析
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本文以115条地震动记录作为输入,计算了R为2、3、4、5这4个不同的屈服强度折减系数下的等强度损伤谱,并以地震动持时20 s为区间划分为5组,每组按平均损伤和平均持时分析地震动持时对结构损伤的影响。
3.1　地震动持时对损伤谱与损伤比谱的影响
本文以R为3、周期为0.2、1.0、3.0 s为例,给出了结构损伤指数和地震动持时的关系,见图4。由图可知,损伤指数随持时增加存在线性递增的趋势,其他周期结果类似。这表明地震动持时对损伤谱的影响是一个连续的过程,如果采用特定数据集的长短持时中位值损伤谱来考虑地震动持时的影响,当地震动持时与数据集的长短持时中位值都相差较远时,可能存在较大的误差。
为了进一步研究地震动持时对结构损伤的影响,采用Pearson积矩相关系数[29]来分析二者间的线性相关性,如式（6）所示：
式中：cov（X,Y）为随机变量X与Y的协方差；XD和YD分别为随机变量X与Y的方差；相关系数r越接近于1,说明线性相关性越明显。本文中X为损伤指数,Y为地震动持时。
本文根据各组均值结构损伤指数以及均值持时,计算得到了不同屈服强度折减系数下各周期点处的Pearson相关系数,结果见图5。除了EPP模型的短周期阶段,各周期点的Pearson相关系数均在0.9~1.0之间,可以认为地震动持时和结构损伤存在较强的线性相关性,这与文献[30]的研究结果一致。
为了进一步研究持时对结构损伤影响随周期的变化规律,本文计算了各组地震动作用下的结构损伤指数与持时最短组的结构损伤指数之比即Ds5-95∈[0,20）s,定义为ρD,如式（7）所示：
本文以屈服强度折减系数R=3为例,展示了各组地震动的等强度损伤谱及比值谱,见图6。由图6（a）、（c）可知,对于EPP和MC这2种滞回模型,当结构自振周期增加时,结构损伤表现出先减小、后增大、再减小的趋势。这是因为在较短周期范围内,即使仅有较小的强度折减,也会导致较大的延性需求和能量耗散需求；而在较长周期范围内,结构相对较柔,地震作用下的结构峰值位移更接近地面位移。同时,随着周期的增加,结构的屈服位移也随之增大,导致延性需求和能量耗散需求逐渐减小,因此在长周期阶段,结构破坏程度随着周期增大而不断减小。
此外,由图6（b）和（d）的比值谱可知,对于EPP滞回模型,结构的破坏程度随着持时的增加而增加,且随自振周期的增大先增加后减少；而对于MC模型,结构的破坏程度同样随着持时的增加而增加,但随自振周期的增大则表现为逐渐减小的趋势,这很可能是因为EPP模型的强度和刚度不会因为屈服而折减,而短周期MC模型的屈服后刚度经历了频繁的折减。
3.2　屈服强度折减系数对损伤谱与损伤比谱的影响
本文对比了在持时为[40,60）s的地震动作用下不同屈服强度折减系数的损伤指数谱,见图7。由图7（a）、（b）可知,对于EPP和MC这2种滞回模型,结构损伤随着屈服强度折减系数的增加而增加,该结果与文献[30]的研究一致,这是由于屈服强度折减系数的增大会使结构屈服更多的次数和更长的时间,并因此增大结构的塑性位移,在滞回过程中耗散更多的能量。为了定量地分析屈服强度折减系数对结构损伤的影响,计算了R在不同取值下的损伤谱与R=2时损伤谱的比值,结果见图7（c）、（d）,对于EPP滞回模型,屈服强度折减系数对损伤谱的影响随结构自振周期的增大而减小；对于MC滞回模型,屈服强度折减系数对损伤谱的影响随着结构自振周期的增大,呈现出先减小后增大再减小的趋势,其他地震动组结果与之类似,这说明屈服强度折减系数对结构损伤指数的影响与结构的滞回模型有关。
另外,为了更好地分析地震动持时对结构地震损伤的影响,本文对比了不同屈服强度折减系数与不同持时地震动组的ρD值,给出了EPP、MC这2种滞回模型下不同屈服强度折减系数的损伤比值谱,见图8。
对于EPP滞回模型,屈服强度折减系数R对ρD的影响随着地震动持时增加而增加。在持时为[20,40）s的地震动作用下,屈服强度折减系数R与比值谱之间无显著规律,而在持时为[80,100）s的地震动作用下,比值谱会随着屈服强度折减系数R的增加而增加,见图8（a）、（d）。而对于MC滞回模型,由图8可知,无论地震动持时的长短,屈服强度折减系数R对比值谱的影响均无明显规律。
4　损伤指数谱预测经验模型
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为了提出更符合真实情况的损伤谱预测模型,本文根据1.2节的记录选取原则,从美国太平洋地震工程中心（Pacific Earthquake Engineering Research Center, PEER）选取了585条不同持时的天然地震动记录,并未对记录进行小波变换等修改,更符合实际情况。所选地震动在各场地上的分布见图9。
由第3节的分析可知,损伤谱受地震动持续时间、屈服强度折减系数和结构恢复力模型的影响。此外,根据文献[13,16],地震动场地也会影响损伤谱。因此,回归分析时需综合考虑这些因素。为了尽量减少天然地震动加速度谱形状差异对损伤谱的影响,本文以天然地震动Ds5-95每隔20 s计算得到的均值损伤谱和均值持续时间为输入,采用差分进化算法进行回归分析,最终得到预测公式。预测公式如式（8）所示：
式中：a、b、c、d、e为待拟合的参数；Ds为Ds5-95。
回归参数和拟合优度见表2,预测值与实际值的对比见图10。EPP模型在各场地的拟合优度分别为0.932、0.912、0.808、0.772、0.935,总拟合优度为0.82, MC模型在各场地的拟合优度分别为0.916、0.932、0.930、0.939、0.948,总拟合优度为0.86。可以看出预测公式在各场地类型上表现均较好,其中MC模型的拟合优度值大多高于EPP模型,这可能是因为MC模型存在结构退化行为,对地震动持时的影响更加敏感。
为了验证预测公式的可靠性和精确性,本文将式（8）与ZHAI等[11]、GHAREHBAGHI等[16]以及MOLAZADEH等[15]提出的预测公式进行对比。在对比时,选取了52条符合所有预测公式应用条件的天然地震动数据,具体信息见表3。为了对比各公式的预测能力,本文采用相对误差来衡量预测效果,计算公式如式（9）所示：
式中：yexact为实际值；ypred为预测值；Re为相对误差。
各预测公式的预测效果,见图11。由图可知,本文的预测公式与实际值的相对误差最小,且相较于其他模型,相对误差降低了至少40%。值得注意的是, ZHAI等[11]和GHAREHBAGHIA等[16]开发的预测模型忽略了地震动持时的影响,因此预测结果相对偏小,而MOLAZADEH等[15]提出的预测公式尽管考虑了地震动持时,但效果并不理想,这可能是由数据集不同、持时考虑方式不同等原因导致。
5　结论
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本文采用谱匹配方法从K-NET强震动数据库中选择了115条不同持时的地震动,并结合EPP和MC这2种滞回模型,计算并分析了不同屈服强度折减系数R下的等强度损伤谱与损伤比谱。随后,从PEER数据库中选取了585条不同场地类型和不同持时的天然地震动,通过差分进化算法提出了损伤谱预测公式。为了验证预测公式的可靠性和准确性,将该公式与已有公式进行了对比,得出如下结论：
1）结构在地震作用下的损伤与持时呈线性正相关,表明在计算损伤谱时,不能忽视持时的影响,且应将其视为一个连续变量加以考虑。此外,结构的自振周期和屈服强度折减系数也会影响持时对损伤谱的作用,因此在分析时应综合考虑这些因素。
2）本文提出的预测公式预测效果良好。其对EPP模型的总拟合优度为0.82,对MC模型的总拟合优度为0.86。在具体的场地类型下,拟合优度不低于0.77。这说明该预测公式能够反映出地震动持时及其他参数对损伤谱的影响。
3）验证结果表明,本文的预测公式与实际值之间的相对误差为0.15,相较于其他预测公式,本文结果的相对误差减小了40%以上,表明本文的预测公式在估计考虑持时的损伤谱时能够更加精确。凸显了在对损伤谱进行预测时考虑持时的必要性。
本文仅以EPP模型和MC模型为例,开展了地震动持时对损伤谱的影响分析,对于其他情况仍需进一步研究。
基金
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  • 国家自然科学基金项目(52178514; U2139209)
  • 国家科技重点研发计划课题省级资助项目(GX18C005)
文献
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参考文献 引证文献
排序方式：
[1]
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杨铭．地震动持时指标与结构响应相关性分析[D]．哈尔滨：中国地震局工程力学研究所, 2020.
YANG Ming. The correlation analysis of structural response with the duration metrics[D]. Harbin: Institute of Engineering Mechanics, China Earthquake Administration, 2020. (in Chinese)
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MOLAZADEH M, SAFFARI H. The effects of ground motion duration and pinching-degrading behavior on seismic response of SDOF systems[J]. Soil Dynamics and Earthquake Engineering, 2018, 114: 333-347.
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2025年第45卷第5期
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doi: 10.13197/j.eeed.2025.0511
  • 接收时间：2024-04-03
  • 首发时间：2026-03-20
  • 出版时间：2025-10-22
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  • 收稿日期：2024-04-03
  • 修回日期：2024-12-09
基金
国家自然科学基金项目(52178514; U2139209)
国家科技重点研发计划课题省级资助项目(GX18C005)
作者信息
    1.中国地震局工程力学研究所地震工程与工程振动重点实验室,黑龙江哈尔滨150080
    2.地震灾害防治应急管理部重点实验室,黑龙江哈尔滨150080

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公茂盛（1976—）,男,研究员,博士,主要从事地震工程研究。E-mail：
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2种不同金属材料的力学参数
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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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