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Article(id=1241793460253037412, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241793456876618047, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2025.0410, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1717516800000, receivedDateStr=2024-06-05, revisedDate=1721145600000, revisedDateStr=2024-07-17, acceptedDate=null, acceptedDateStr=null, onlineDate=1773996232329, onlineDateStr=2026-03-20, pubDate=1755792000000, pubDateStr=2025-08-22, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773996232329, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773996232329, creator=13701087609, updateTime=1773996232329, updator=13701087609, issue=Issue{id=1241793456876618047, tenantId=1146029695717560320, journalId=1241701559352995854, year='2025', volume='45', issue='4', pageStart='1', pageEnd='222', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773996231526, creator=13701087609, updateTime=1773997043565, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241796862877958695, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241793456876618047, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241796862877958696, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241793456876618047, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=94, endPage=101, ext={EN=ArticleExt(id=1241793461523911529, articleId=1241793460253037412, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Seismic damage analysis of loess slopes based on vibration velocity, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

To address the significant discrepancy between damage degree and peak values when employing traditional acceleration indices for evaluating seismic damage in loess slopes under large earthquakes at far-field and small earthquakes at near-field scenarios, this study developed a novel evaluation system based on particle vibration velocity theory. Through shaking model tests and numerical simulations, the coupling mechanisms between acceleration and velocity responses during seismic damage evolution in loess slopes were systematically investigated, revealing intrinsic correlations between dynamic parameters and damage states. The results indicate the acceleration amplification effect of loess slopes is obvious. When the peak acceleration is taken as the evaluation index, the calculated intensity of loess slope top in the near field is greater than the actual intensity. A linear correlation was established between peak particle velocity and soil tensile strength. It is suggested that the peak velocity should be used as the evaluation index of failure intensity for loess slope with typical site amplification effect. An innovative five-level seismic intensity evaluation system was proposed in accordance with GB/T 17742—2020 specifications, defining velocity threshold intervals and characteristic failure patterns for each damage level, thereby establishing a quaternion correspondence criterion integrating damage degree, intensity, peak velocity, and seismic damage characteristics. This research provides theoretical foundations and quantitative criteria for seismic damage assessment of loess slopes.

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针对传统加速度指标在评价大震远场与小震近场边坡地震损伤时存在的破坏程度与峰值离散性显著问题，该文基于质点振动速度理论构建了黄土边坡损伤新型评价体系。通过振动台模型试验与数值模拟相结合的方法，分析了黄土边坡地震损伤演化过程中加速度与速度响应的耦合规律，揭示了动力参数与损伤状态的关联机制。研究结果表明：黄土边坡的加速度放大效应明显，以加速度峰值为评价指标时，位于近场的黄土边坡坡顶计算烈度大于实际烈度。地震动速度与土体抗拉强度间存在线性相关关系，具有典型场地放大效应的黄土边坡建议采用速度峰值作为破坏烈度的评价指标。结合GB/T 17742—2020《中国地震烈度表》，提出包含5级损伤状态的黄土边坡地震烈度评价体系，界定各损伤等级对应的速度阈值区间及典型破坏形态，建立边坡损伤程度-烈度-速度峰值-宏观震害的四元对应准则。研究成果为黄土地区边坡地震损伤评估提供了新的理论依据和量化判据。

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王丽丽（1988—），女，副研究员，博士，主要从事岩土地震工程研究。E-mail：

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王丽丽（1988—），女，副研究员，博士，主要从事岩土地震工程研究。E-mail：

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王丽丽（1988—），女，副研究员，博士，主要从事岩土地震工程研究。E-mail：

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(in Chinese), articleTitle=Testing Study on relationship among p-wave velocity and physico-mechanical in xiashu loess, refAbstract=null), Reference(id=1241802922678353990, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, doi=null, pmid=null, pmcid=null, year=2003, volume=null, issue=null, pageStart=183, pageEnd=208, url=null, language=null, rfNumber=[18], rfOrder=34, authorNames=王兰民, journalName=黄土动力学, refType=null, unstructuredReference=王兰民. 黄土动力学[M]. 北京：地震出版社，2003：183-208., articleTitle=null, refAbstract=null), Reference(id=1241802922787405906, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, doi=null, pmid=null, pmcid=null, year=2003, volume=null, issue=null, pageStart=183, pageEnd=208, url=null, language=null, rfNumber=[18], rfOrder=35, authorNames=WANG Lanmin, journalName=Loess dynamics, refType=null, unstructuredReference=WANG Lanmin. Loess dynamics[M]. 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accelerometers in the shaking table model test, figureFileSmall=PtbYqALRtm640Vn+a2jXhQ==, figureFileBig=VAIOou/jJEaOIakRW51LMw==, tableContent=null), ArticleFig(id=1241802909462102191, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=CN, label=图1, caption=振动台模型试验加速度传感器分布图, figureFileSmall=PtbYqALRtm640Vn+a2jXhQ==, figureFileBig=VAIOou/jJEaOIakRW51LMw==, tableContent=null), ArticleFig(id=1241802909638262978, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=EN, label=Fig. 2, caption=Velocity time history curves of measuring point A6 at the slope top under working condition 5 (PGA<2.5 m/s2), figureFileSmall=zMHBiuMlppS1dZTqapVSlA==, figureFileBig=QpdOOniBPH+KF3weHKfqVg==, tableContent=null), ArticleFig(id=1241802909768286417, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=CN, label=图2, caption=工况5（PGA<2.5 m/s2）坡顶测点A6速度时程曲线, 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tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=CN, label=图7, caption=坡顶测点速度峰值和加速度峰值关系曲线, figureFileSmall=MzneUvqRa5KL0p/N+rAcMA==, figureFileBig=0MLMsH3ywjmTncq1wsvoDQ==, tableContent=null), ArticleFig(id=1241802912804962684, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=EN, label=Table 1, caption=

Loading conditions for the shaking table test

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工况地震波台面加速度峰值/（m/s2）烈度工况地震波台面加速度峰值/（m/s2）烈度
工况1正弦扫频（0.1~50 Hz）0.50Ⅵ工况5压缩波2.50Ⅷ
工况2压缩波0.86Ⅵ工况6原场波3.76Ⅷ
工况3原场波0.74Ⅵ工况7原场波5.40Ⅸ
工况4原场波1.30Ⅶ工况8原场波7.38Ⅸ
), ArticleFig(id=1241802912964346252, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=CN, label=表1, caption=

振动台试验加载工况

, figureFileSmall=null, figureFileBig=null, tableContent=
工况地震波台面加速度峰值/（m/s2）烈度工况地震波台面加速度峰值/（m/s2）烈度
工况1正弦扫频（0.1~50 Hz）0.50Ⅵ工况5压缩波2.50Ⅷ
工况2压缩波0.86Ⅵ工况6原场波3.76Ⅷ
工况3原场波0.74Ⅵ工况7原场波5.40Ⅸ
工况4原场波1.30Ⅶ工况8原场波7.38Ⅸ
), ArticleFig(id=1241802913140507031, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=EN, label=Table 2, caption=

Scale of earthquake intensity in GB/T 17742—2020

, figureFileSmall=null, figureFileBig=null, tableContent=
破坏现象描述烈度PGV/（m/s）PGA/（m/s2）破坏现象描述烈度PGV/（m/s）PGA/（m/s2）
河岸和松软土地出现裂缝Ⅵ0.0557
0.038~0.082		0.653
0.457~0.963		干硬土地裂缝较多，滑坡常见Ⅸ0.555
0.379~0.814		5.770
4.020~8.300
河岸出现塌方，松软土地裂缝增多Ⅶ0.120
0.082~0.176		1.350
0.937~1.94		山崩和地震断裂出现Ⅹ1.190
0.815~1.750		11.900
8.310~17.200
干硬土地出现裂缝Ⅷ0.258
0.177~0.378		2.790
1.950~4.010		地震断裂连续很大，大量山崩滑坡Ⅺ2.570
1.760~3.770		24.700
17.300~35.500
), ArticleFig(id=1241802913291501997, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=CN, label=表2, caption=

GB/T 17742—2020《中国地震烈度表》[15]

, figureFileSmall=null, figureFileBig=null, tableContent=
破坏现象描述烈度PGV/（m/s）PGA/（m/s2）破坏现象描述烈度PGV/（m/s）PGA/（m/s2）
河岸和松软土地出现裂缝Ⅵ0.0557
0.038~0.082		0.653
0.457~0.963		干硬土地裂缝较多，滑坡常见Ⅸ0.555
0.379~0.814		5.770
4.020~8.300
河岸出现塌方，松软土地裂缝增多Ⅶ0.120
0.082~0.176		1.350
0.937~1.94		山崩和地震断裂出现Ⅹ1.190
0.815~1.750		11.900
8.310~17.200
干硬土地出现裂缝Ⅷ0.258
0.177~0.378		2.790
1.950~4.010		地震断裂连续很大，大量山崩滑坡Ⅺ2.570
1.760~3.770		24.700
17.300~35.500
), ArticleFig(id=1241802913429914045, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=EN, label=Table 3, caption=

PGA and PGV at the top of loess slope

, figureFileSmall=null, figureFileBig=null, tableContent=
坡体损伤特征损伤程度坡顶
PGV /（m/s）		坡顶
PGA /（m/s2）		台面
PGA /（m/s2）
坡脚处发现轻微落土基本完好0.0922.660.74
坡顶和“土-结构”相互作用部位出现张拉裂缝轻微破坏0.21416.402.50
坡顶张拉横向裂缝扩展和水平贯通（坡面中下部出现局部破损掉块）中等破坏0.60519.093.76
坡顶产生小规模滑坡严重破坏0.97229.305.40
坡顶产生大规模滑坡毁坏1.04926.037.38
), ArticleFig(id=1241802913614463432, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=CN, label=表3, caption=

黄土边坡坡顶地震动速度峰值与加速度峰值

, figureFileSmall=null, figureFileBig=null, tableContent=
坡体损伤特征损伤程度坡顶
PGV /（m/s）		坡顶
PGA /（m/s2）		台面
PGA /（m/s2）
坡脚处发现轻微落土基本完好0.0922.660.74
坡顶和“土-结构”相互作用部位出现张拉裂缝轻微破坏0.21416.402.50
坡顶张拉横向裂缝扩展和水平贯通（坡面中下部出现局部破损掉块）中等破坏0.60519.093.76
坡顶产生小规模滑坡严重破坏0.97229.305.40
坡顶产生大规模滑坡毁坏1.04926.037.38
), ArticleFig(id=1241802913790624220, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=EN, label=Table 4, caption=

Modified PGV considering slope amplification effect in GB/T 17742—2020

, figureFileSmall=null, figureFileBig=null, tableContent=
破坏现象描述烈度1.22 PGV/（m/s）破坏现象描述烈度1.22 PGV/（m/s）
河岸和松软土地出现裂缝Ⅵ0.055~0.990干硬土地裂缝较多，滑坡常见Ⅸ0.462~0.993
河岸出现塌方，松软土地裂缝增多Ⅶ0.100~0.215山崩和地震断裂出现Ⅹ0.994~2.135
干硬土地出现裂缝Ⅷ0.216~0.461地震断裂连续很大，大量山崩滑坡Ⅺ2.136~4.599
), ArticleFig(id=1241802913941619176, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=CN, label=表4, caption=

GB/T 17742—2020考虑边坡放大效应的PGV值

, figureFileSmall=null, figureFileBig=null, tableContent=
破坏现象描述烈度1.22 PGV/（m/s）破坏现象描述烈度1.22 PGV/（m/s）
河岸和松软土地出现裂缝Ⅵ0.055~0.990干硬土地裂缝较多，滑坡常见Ⅸ0.462~0.993
河岸出现塌方，松软土地裂缝增多Ⅶ0.100~0.215山崩和地震断裂出现Ⅹ0.994~2.135
干硬土地出现裂缝Ⅷ0.216~0.461地震断裂连续很大，大量山崩滑坡Ⅺ2.136~4.599
), ArticleFig(id=1241802914038088180, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=EN, label=Table 5, caption=

Seismic damage discrimination table for loess slopes based on vibration velocity

, figureFileSmall=null, figureFileBig=null, tableContent=
坡体损伤特征损伤程度烈度PGV /（m/s）
坡脚处发现轻微落土基本完好Ⅵ0.055~0.990
坡顶和“土-结构”相互作用部位出现张拉裂缝轻微破坏Ⅶ0.100~0.215
坡顶张拉横向裂缝扩展和水平贯通（坡面中下部出现局部破损掉块）中等破坏Ⅷ0.216~0.605
坡顶产生滑动破坏严重破坏Ⅸ0.606~0.993
边坡产生大规模滑坡毁坏Ⅹ0.994~2.135
), ArticleFig(id=1241802914163917310, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241793460253037412, language=CN, label=表5, caption=

基于地震动速度的黄土边坡地震损伤判别表

, figureFileSmall=null, figureFileBig=null, tableContent=
坡体损伤特征损伤程度烈度PGV /（m/s）
坡脚处发现轻微落土基本完好Ⅵ0.055~0.990
坡顶和“土-结构”相互作用部位出现张拉裂缝轻微破坏Ⅶ0.100~0.215
坡顶张拉横向裂缝扩展和水平贯通（坡面中下部出现局部破损掉块）中等破坏Ⅷ0.216~0.605
坡顶产生滑动破坏严重破坏Ⅸ0.606~0.993
边坡产生大规模滑坡毁坏Ⅹ0.994~2.135
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基于地震动速度的黄土边坡地震损伤分析
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王丽丽 1, 2 , 王兰民 2 , 王平 2 , 许世阳 2, 3, 4
地震工程与工程振动 | 2025,45(4): 94-101
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地震工程与工程振动 | 2025, 45(4): 94-101
基于地震动速度的黄土边坡地震损伤分析
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王丽丽1, 2 , 王兰民2, 王平2, 许世阳2, 3, 4
作者信息
  • 1.西北大学 地质学系，陕西 西安 710069
  • 2.中国地震局兰州地震研究所，甘肃 兰州 730000
  • 3.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
  • 4.地震灾害防治应急管理部重点实验室，黑龙江 哈尔滨 150080

    • 王丽丽（1988—），女，副研究员，博士，主要从事岩土地震工程研究。E-mail：

Seismic damage analysis of loess slopes based on vibration velocity
Lili WANG1, 2 , Lanmin WANG2, Ping WANG2, Shiyang XU2, 3, 4
Affiliations
  • 1.Department of Geology, Northwest University, Xi’an 710069, China
  • 2.Lanzhou Institute of Seismology, China Earthquake Administration, Lanzhou 730000, China
  • 3.Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
  • 4.Key Laboratory of Earthquake Disaster Mitigation, Ministry of Emergency Management, Harbin 150080, China
出版时间: 2025-08-22 doi: 10.13197/j.eeed.2025.0410
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针对传统加速度指标在评价大震远场与小震近场边坡地震损伤时存在的破坏程度与峰值离散性显著问题，该文基于质点振动速度理论构建了黄土边坡损伤新型评价体系。通过振动台模型试验与数值模拟相结合的方法，分析了黄土边坡地震损伤演化过程中加速度与速度响应的耦合规律，揭示了动力参数与损伤状态的关联机制。研究结果表明：黄土边坡的加速度放大效应明显，以加速度峰值为评价指标时，位于近场的黄土边坡坡顶计算烈度大于实际烈度。地震动速度与土体抗拉强度间存在线性相关关系，具有典型场地放大效应的黄土边坡建议采用速度峰值作为破坏烈度的评价指标。结合GB/T 17742—2020《中国地震烈度表》，提出包含5级损伤状态的黄土边坡地震烈度评价体系，界定各损伤等级对应的速度阈值区间及典型破坏形态，建立边坡损伤程度-烈度-速度峰值-宏观震害的四元对应准则。研究成果为黄土地区边坡地震损伤评估提供了新的理论依据和量化判据。

地震  /  黄土边坡  /  地震动速度  /  损伤分析  /  加速度峰值

To address the significant discrepancy between damage degree and peak values when employing traditional acceleration indices for evaluating seismic damage in loess slopes under large earthquakes at far-field and small earthquakes at near-field scenarios, this study developed a novel evaluation system based on particle vibration velocity theory. Through shaking model tests and numerical simulations, the coupling mechanisms between acceleration and velocity responses during seismic damage evolution in loess slopes were systematically investigated, revealing intrinsic correlations between dynamic parameters and damage states. The results indicate the acceleration amplification effect of loess slopes is obvious. When the peak acceleration is taken as the evaluation index, the calculated intensity of loess slope top in the near field is greater than the actual intensity. A linear correlation was established between peak particle velocity and soil tensile strength. It is suggested that the peak velocity should be used as the evaluation index of failure intensity for loess slope with typical site amplification effect. An innovative five-level seismic intensity evaluation system was proposed in accordance with GB/T 17742—2020 specifications, defining velocity threshold intervals and characteristic failure patterns for each damage level, thereby establishing a quaternion correspondence criterion integrating damage degree, intensity, peak velocity, and seismic damage characteristics. This research provides theoretical foundations and quantitative criteria for seismic damage assessment of loess slopes.

earthquake  /  loess slope  /  vibration velocity  /  damage analysis  /  peak acceleration
王丽丽, 王兰民, 王平, 许世阳. 基于地震动速度的黄土边坡地震损伤分析. 地震工程与工程振动, 2025 , 45 (4) : 94 -101 . DOI: 10.13197/j.eeed.2025.0410
Lili WANG, Lanmin WANG, Ping WANG, Shiyang XU. Seismic damage analysis of loess slopes based on vibration velocity[J]. Earthquake Engineering and Engineering Dynamics, 2025 , 45 (4) : 94 -101 . DOI: 10.13197/j.eeed.2025.0410
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0　引言
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烈度是衡量岩土场地与建（构）筑物在地震作用下破坏程度的重要指标，边坡的烈度可概括为地震作用下边坡的破坏程度。目前，关于烈度与地震动参数相关性的研究已经有众多文献发表，包括烈度与加速度峰值（peak ground acceleration，PGA）的研究、烈度与速度峰值（peak ground velocity，PGV）的研究、烈度与持时的研究、烈度与反应谱的研究等等。其中，地震动峰值加速度PGA与地震动峰值速度PGV是最方便获取、被广大科研工作者广泛接受的评价指标，因此，美国USGS与我国的烈度速报系统中都采用了PGA与PGV作为计算烈度的参数。
加速度峰值PGA本质上是惯性力的体现（F=ma），而速度是波的能量的体现（w=0.5 mv2）。近年来，理论研究与实际震害经验都表明：采用加速度评价场地与建（构）筑物的破坏程度时，在大震远场、小震近场与局部地形中，会产生破坏程度与加速度峰值离散性较大的问题，导致PGA量值与破坏程度不符。例如，在2008年汶川地震Ⅷ度区内的汉源九襄台台站测得的地震动峰值加速度PGA为0.83 m/s2，地震动峰值明显与烈度不符[1]，其主要原因是场地受土层结构、地形效应以及断裂带的影响，造成了破坏效应的放大；在2013年庐山MS7.0地震中，在Ⅶ度区某台站测得的基岩PGA超过1 g，PGV小于0.25 m/s2，但该台站周围建筑物的破坏非常轻微，经查此测点位于山坡上，山坡的高程放大效应造成了该测点PGA值的异常，速度峰值较小，与现场建筑的破坏程度相吻合[2]；又如2008年汶川地震在甘肃等多个地方测得的PGA很小，而PGV很大，建筑发生了较为严重的破坏，这是因为大震远场的地震波长周期效应导致的破坏效应增强[3]；在一些小震中，经常发现近场PGA值过大的情况，这主要是因为近场地震波高频成分过多，导致PGA出现了尖峰效应。
HOUSNER等[4]、叶列平等[5]指出，目前较多采用的PGA指标虽然对周期较短的结构适用，但是中长周期结构地震响应与PGA指标的相关性较差，用于中高层结构抗震性能评价时，会导致分析结果的离散程度较大，给抗震性能评价带来不准确性。黄土地区受沟壑纵横的地形地貌影响，存在大量的高边坡，这些边坡有自振周期长、场地放大效应明显的特点[6~7]，因此，PGV指标对长周期的黄土高边坡适用性更好，是基于性能设计和评价较为合适的地震动强度指标，2008年汶川8.0地震、2013年芦山7.0级地震、2021年云南漾濞6.4级地震的数据研究皆支持了该结论[2，5，8-9]。杜陆荣等[10]随机选取了100条加速度时程地震波，通过积分计算得到了不同地震波的速度峰值（PGV）、位移峰值（peak ground displacement，PGD），通过统计分析地震波的PGV、PGD与边坡土体坡面不同测点的响应位移之间的关联性，得到了PGA、PGV、PGD相关系数的平均值分别为0.868、0.980、0.926，因此，PGV与位移响应间的相关性最好，建议在边坡稳定性评价中以PGV作为参数指标。
中国烈度速报系统在低烈度（IA和IV有一个小于6时）采用I=（IA+IV）/2的方法，同时体现PGA与PGV的评价效果，在高烈度（IA和IV均大于6时）采用PGV的计算结果作为仪器烈度，有效避免产生大震PGA近震中异常高烈度的情况（I为烈度，IA指应用PGA得到的地震烈度计算值，IV指应用PGV得到的地震烈度计算值）。综上所述，采用地震动峰值速度作为评价指标来评价边坡破坏程度是极具理论与实践意义的。本文在厘清地震动速度与土体的抗拉强度间关系的基础上，以地震动速度为评价指标，通过振动台模型试验，建立了黄土边坡破坏特征与地震动速度的对应准则，对黄土边坡的破坏状态进行了评价和划分。
1　地震动速度作为边坡损伤程度评价指标的合理性
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在坡面上，引起临空面放大效应和坡面局部破坏的主要原因是地震波在坡面的反射作用。反射波的形成是压应力波反射转变为拉应力波的过程，由于土体的抗拉强度很小，所以反射波在自由面上会引起一系列的破坏。从地震波的传播理论出发，根据一维弹性应力波理论，坡面上任意一点的位移如式（1）所示：
对应的速度可表示为
而一点处的应变可表示为
因此，由式（2）和式（3）可建立波动产生的动应力与质点地震动速度间的关系为
式（4）与基于最大应力理论的爆破振动的峰值质点速度Vpp（peak particle velocity，PPV）损伤判据公式接近，表达式[11-12]为
式中：Cp为土体纵波波速；ε为土体极限拉应变；E为弹性模量；σt为土体抗拉强度。
由此可知，地震动速度与土体的抗拉强度间存在直接的线性关系，而抗拉强度为岩土体的一种固有力学属性，黄土的抗拉强度较低，因此采用速度作为评价指标，可直观地体现坡体的破坏程度。由于质点振动速度PPV起源于爆破振动，地震波引起的坡面破坏还涉及波的透射、反射和折射等波动效应，因此文中统一用速度峰值PGV来体现地震波在坡体表面的震动效应。
为了验证以上理论推导在黄土边坡地震损伤判别中应用的合理性，进行了大型振动台模型试验，具体的模型制作、破坏过程和加速度响应分析在文献[13-14]中有详细介绍。试验地震波采用汶川地震在陕西省西安市蓝田县汤峪镇采集到的远场波，考虑地震波的动力相似时，将地震波压缩7.07倍，不考虑地震波的动力相似时，采用地震波的原始加速度时程。试验加载工况表见表1，其中的烈度为GB/T 17742—2020《中国地震烈度表》[15]中台面加速度峰值对应的烈度。模型按照地震动强度从小到大共加载8个有效工况，具体的加载工况见表1。
在该模型试验中，模型在工况5（PGA<2.5 m/s2）时破坏不明显，边坡模型在PGA为2.50 m/s2地震波作用下坡顶测点A6附近产生首条横向裂缝，见图1。以测点A6的速度峰值PGV作为质点振动速度临界值，若通过式（5）计算所得值与测点A6的实测值接近，则说明以质点地震动速度评价黄土边坡破坏程度是合理可行的。工况5（PGA<2.5 m/s2）坡顶测点A6的速度时程曲线见图2。
由图2可知，PGA为2.50 m/s2地震波作用下测点A6黄土边坡坡顶地震损伤临界速度为0.21 m/s。根据金敏[16]的研究结果，黄土层纵波波速与土体密度间的线性关系为
根据式（6）计算得到试验模型的纵波波速为502.3 m/s，这一计算结果与王峥辉等[17]提出的土体纵波波速Cp为524~1442 m/s（土体含水率不同）的结果相近。取弹性模量E=36.35 MPa[18]，土体抗拉强度σt=11.6 kPa[19]，则计算所得黄土的地震损伤临界速度为0.17~0.46 m/s，实测得到的黄土边坡坡顶地震损伤临界速度数值在此范围中，验证了黄土边坡采用地震动速度判定边坡破坏状态的合理性。
2　黄土边坡PGA与PGV响应规律对比分析
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2.1　黄土边坡地震动失稳损伤特征
综合考虑坡顶建筑的安全性与边坡的破坏程度，将地震荷载作用下黄土建筑边坡的损伤过程划分为5个阶段：
1）第1阶段：基本完好，坡脚处发现轻微落土（工况1~工况4）。
2）第2阶段：轻微破坏，坡顶和“土-结构”相互作用部位出现张拉裂缝（工况5）。
3）第3阶段：中等破坏，坡顶张拉横向裂缝扩展和水平贯通，坡面中下部出现局部破损掉块（工况6）。
4）第4阶段：严重破坏，坡顶产生少量滑动破坏（工况7）。
5）第5阶段：毁坏，边坡产生大规模滑动破坏，建筑产生向临坡一侧的倾斜（工况8）。
边坡不同破坏阶段的典型破坏见图3。
2.2　加速度与速度响应分析
通过对加速度时程曲线进行积分得到速度时程曲线。在边坡产生滑动破坏前，提取不同地震动强度作用下坡面各测点的速度峰值PGV随坡面高程的变化曲线见图4，求解速度时程曲线过程中进行了基线校正和滤波处理，保留了0.1~25 Hz频段内的波形。同时，对比分析坡面加速度与速度的变化趋势，坡面测点对应的加速度峰值PGA见图5。纵坐标h/H为测点高程与边坡高度的比值。
对比分析图4、图5可知，速度时程曲线与加速度时程曲线的变化趋势不同，在压缩波（PGA为0.86、2.50 m/s2）作用下，加速度沿高程方向整体呈逐渐增大的变化趋势，速度在坡肩和坡脚处较大，此时边坡处于基本完好和轻微破坏阶段，分别以坡脚处的落土和坡肩处的张拉裂隙为主；在原场波（PGA为3.76 m/s2）作用下，加速度沿高程方向仍然呈逐渐增大的变化规律，而速度在0.57倍坡高处突增，此时边坡处于中等破坏阶段，坡面距离坡底0.43倍高程处出现水平向裂缝，并产生局部的破损掉块，这与速度峰值在坡面突增的位置接近。由此可知，坡面速度峰值PGV的变化趋势与破坏分布特征相关性比加速度好，可以有效反应模型的破坏状态。
GB/T 17742—2020《中国地震烈度表》[15]中烈度Ⅵ~Ⅸ对应的仪器加速度峰值与速度峰值及部分现象描述，见表2。
对比分析图4、图5与表2可知：
1）以加速度峰值PGA为评价指标时，相较于台面加速度，坡顶烈度普遍增大Ⅱ~Ⅲ度。地震波强度越小，坡顶加速度峰值放大越明显。
2）以速度峰值PGV为评价指标时，坡顶的速度峰值PGV与表2中破坏烈度及破坏现象描述接近，如台面加速度PGA为2.5 m/s2时，坡肩处的PGV为0.2 m/s，此时坡顶出现裂缝，坡肩处的PGV值以及台面的PGA皆对应烈度Ⅷ，而坡肩处的PGA对应的破坏烈度为Ⅺ度，采用PGA作为烈度评价指标时，烈度增大了Ⅲ度，实际破坏现象与表2中的破坏现象不符。由此可知，对加速度放大效应特别明显的黄土边坡，以加速度峰值PGA作为烈度评价指标时，会放大该处的地震烈度，以速度峰值PGV作为破坏烈度的评价指标更合理。
建立与模型试验相对应的三维有限元数值模型，坡顶建筑的临坡距离d分别设置为5、20、35 m，提取坡面的速度峰值见图6。
由图6可知，数值计算中坡面的速度时程曲线变化趋势与图4模型试验压缩波（PGA为0.86、2.50 m/s2）作用下坡面的速度时程曲线变化规律一致，说明对模型试验结果的分析是准确的。同时，数值计算中使用的是原场波，且数值计算模型是非缩尺的足尺模型，其曲线的变化趋势与模型试验中压缩波的趋势一致。由此可知，模型试验中考虑动力相似是极为重要的，这影响到模型的动力响应规律是否能够反映原型实际情况。
3　黄土边坡地震失稳损伤判别方法
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地震荷载作用下坡顶的测点A6和测点A7附近最先产生了横向裂缝，因此坡顶的速度峰值在PGA<5.40 m/s2时以测点A6为代表（测点A6在PGA为5.40 m/s2时被抛出），PGA为7.38 m/s2时以测点A7为代表，5个破坏过程代表着模型的5种损伤程度，将破坏过程中的破坏现象与对应的加速度峰值PGA和速度峰值PGV进行统计分析，见表3。
对比分析表2与表3可知：
1）表3中从轻微破坏到毁坏的5种损伤程度与表2中5种烈度对应的破坏现象基本是对应的。如：表3损伤程度毁坏时边坡产生大规模滑坡，对应表2中Ⅹ度的破坏现象为山崩；表3损伤程度严重破坏时边坡产生小规模滑坡，对应表2中Ⅸ度的破坏现象为滑坡常见；表3破坏程度中等时裂缝扩展、边坡产生局部破坏，对应表2中Ⅶ度破坏为河岸出现塌方、裂缝增多。
2）从PGV对应的烈度来看，表3中基本完好对应表2中Ⅵ度，表3中轻微破坏对应表2中Ⅶ度，表3中等破坏对应表2中Ⅷ度，表3中严重破坏对应表2中Ⅸ度，表3中毁坏对应表2中Ⅹ度。
3）从PGA对应的烈度来看，相同烈度下，边坡台面的PGA值与GB/T 17742—2020《中国地震烈度表》中的PGA值接近，坡面与坡顶处的PGA值远大于GB/T 17742—2020《中国地震烈度表》中的PGA值，这种规律在小震的情况下更加明显，采用PGA为量化指标得到的边坡场地烈度远大于GB/T 17742—2020《中国地震烈度表》中的烈度值。
4）表3中坡体损伤程度所对应的速度临界值PGV仍然略大于GB/T 17742—2020《中国地震烈度表》中的地震烈度对应的PGV值，其原因：一是因为边坡场地的高程放大效应导致的速度值的增大，二是根据丁保荣等[2]对中国、美国、墨西哥和伊朗共97次地震中PGV及其烈度等相关资料的研究成果，其比对了美国USGS与日本的PGV判别阈值，认为我国烈度表中不同烈度下的PGV偏低（最新的2020版中的PGV与2008版变化幅值不大）。
工况2~工况7的测点A6的PGV与测点A1比值的平均值为1.22，即测点A6（坡顶）的速度峰值比坡下水平场地放大了1.22倍，因此，按照此系数将表2中PGV提高1.22倍后得到了表4。对于有明显放大效应的场地采用放大系数进行烈度调整的方法在我国第五代区划图上也有应用，在编制过程中，以I1类场地地震动参数为基础，通过放大系数调整表，换算得到Ⅱ类场地地震动参数区划结果[20]。因此，按照速度放大系数，将表2的速度峰值提高1.22倍的研究方法是合理的。
对比分析表3与表4可知，表3中的PGV数据与考虑边坡放大效应的表4数据极为接近。黄土边坡基本完好对应Ⅵ度破坏（PGV为0.055~0.99 m/s），轻微破坏可对应Ⅶ度破坏（PGV为0.100~0.215 m/s），中等破坏可对应Ⅷ度~Ⅸ度破坏（PGV为0.216~0.605 m/s），严重破坏可对应Ⅸ度破坏（PGV为0.606~0.993 m/s），毁坏可对应Ⅹ度破坏（PGV为0.994~2.135 m/s）。综合表3中的破坏特征与损伤程度以及表4中的烈度与PGV值，提出黄土边坡坡顶与坡面地震失稳损伤判别见表5。
将表3中坡顶速度峰值与对应的台面（基岩）PGA之间的关系曲线进行汇总，见图7。
由图7可知，坡顶的地震动速度随着输入地震动强度的增加逐渐趋于稳定和饱和，这是因为土体的抗拉强度存在极限值，速度达到坡体某测点的抗拉强度极值后，坡体发生破坏，因此黄土边坡的地震破坏烈度最大划分至Ⅹ度，此时边坡已经发生大规模的滑动破坏。同时，目前已有地震实例证明了表5在评定边坡烈度方面的合理性。如：2013年4月20日，在芦山MS7.0级地震中，震中附近的位于山坡之上的051BXD台站捕获了PGA超过1 g的记录，但研究人员现场调查后发现该区域震害并不严重，宏观烈度仅为Ⅶ度，但是峰值速度PGV分量均低于25 cm/s[21]，与文中表5提出的速度区间以及烈度评定结果一致。2014年鲁甸地震震中区域的053LLT台站同样捕获了接近1 g的记录，但是水平PGV分量均超过了75 cm/s，现场调查发现附近建筑破坏十分严重，所在区域宏观烈度高达Ⅸ度[22]，这一结果也与表5给出的烈度建议值与速度峰值取值范围一致。以上震害实例证明了表5研究结果的合理性。
4　结论
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1）黄土边坡的加速度放大效应明显，以加速度峰值PGA为评价指标时，对照现有国标得到的计算烈度大于实际震害烈度Ⅱ度~Ⅲ度。地震动强度越小，位于近场的黄土边坡的这种放大规律越明显。
2）临界地震动速度与土体抗拉强度间存在线性相关关系，具有典型场地放大效应的黄土边坡应采用速度峰值PGV作为破坏烈度的评价指标。
3）根据振动台模型试验边坡的实际破坏状态与对应的速度峰值，结合GB/T 17742—2020《中国地震烈度表》中的相关规定，提出了黄土边坡损伤特征、损伤程度、计算烈度及速度间的对应标准。
本文基于质点振动速度理论，通过振动台模型试验和数值模拟，对比分析了加速度峰值和速度峰值在边坡烈度评定时的优缺点，建立了黄土边坡破坏特征、损伤程度、烈度、速度峰值间的对应关系，提出了黄土边坡地震失稳损伤判别表，对于震后黄土地区的烈度评定与震损评估研究具有帮助，是从破坏特征与地震动速度角度对具有典型场地放大效应的黄土边坡进行地震损伤快速判别的一次尝试。由于模型试验和数值模拟场地特征的单一性以及选取汶川地震波为代表性地震波，后期还需要将边坡按照上覆土层厚度和基岩埋深等关键影响因素进行划分，给出不同类型黄土边坡放大系数调整表，结合地震现场实例和数值模拟，丰富样本空间来完善文中提出的黄土边坡地震失稳损伤判别标准。文中得到的“基于地震动速度的黄土边坡地震失稳损伤判别表”坡体损伤特征中增加了“土-结构”相互作用处破坏的描述，是考虑了西北黄土地区坡顶有建筑存在时的特殊情况。
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  • 国家自然科学基金项目(4232320; U1939209)
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2025年第45卷第4期
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doi: 10.13197/j.eeed.2025.0410
  • 接收时间：2024-06-05
  • 首发时间：2026-03-20
  • 出版时间：2025-08-22
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  • 收稿日期：2024-06-05
  • 修回日期：2024-07-17
基金
国家自然科学基金项目(4232320; U1939209)
作者信息
    1.西北大学 地质学系，陕西 西安 710069
    2.中国地震局兰州地震研究所，甘肃 兰州 730000
    3.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
    4.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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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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