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Article(id=1241794072449454144, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241794070289387562, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2025.0513, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1715011200000, receivedDateStr=2024-05-07, revisedDate=1725897600000, revisedDateStr=2024-09-10, acceptedDate=null, acceptedDateStr=null, onlineDate=1773996378290, onlineDateStr=2026-03-20, pubDate=1761062400000, pubDateStr=2025-10-22, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773996378290, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773996378290, creator=13701087609, updateTime=1773996378290, 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=131, endPage=141, ext={EN=ArticleExt(id=1241794072726278213, articleId=1241794072449454144, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Vulnerability analysis of gravity dams based on comprehensive damage index under near-fault earthquake action, columnId=1241794071602200899, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

Existing studies have shown that near-fault impulsive ground motions have a significant impact on the seismic performance of concrete gravity dams. However, current research on the vulnerability of concrete gravity dams under near-fault ground motions remains limited, and most studies use a single response parameter as the performance indicator, which makes it difficult to comprehensively characterize the seismic performance of gravity dams. Taking a certain engineering concrete gravity dam as an example, this paper establishes a unified plastic damage model of the dam-foundation system. Multiple measured near-fault impulsive and non-impulsive ground motions are selected. Then, it calculates the comprehensive damage index of the gravity dam is calculated using the method of efficacy coefficient combined with the modified weighting model. A logarithmic probability seismic demand model is established for PGA (peak ground acceleration) and three single indices including accumulated base sliding, relative displacement of the dam crest, and overall damage index, as well as a comprehensive response index. By combining the criteria for dividing damage levels for each index, vulnerability curves are obtained. The paper compares the characteristics of near-fault ground motion pulses and the influence of single and comprehensive response indices on the seismic performance of concrete gravity dams. The results indicate that the probability of concrete gravity dams experiencing minor, moderate, and severe damage under near-fault impulsive ground motions is higher than that under non-impulsive ground motions. Evaluating seismic performance using a single index may lead to overestimation of the dam's seismic resistance under certain PGAs. Using a comprehensive damage index as the performance indicator for evaluating the probability of damage and ultimate seismic capacity of gravity dams is more reasonable.

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近断层脉冲型地震动对混凝土重力坝抗震性能有重要影响,然而,目前对近断层地震动作用下混凝土重力坝的易损性研究较少,且均以单一响应指标为性能指标,难以全面表征重力坝的抗震性能。该文以某工程混凝土重力坝为例,建立坝体-地基整体塑性损伤模型。通过选取多条实测近断层脉冲型和非脉冲型地震动,依据功效系数法加变权模型的方式计算得到重力坝综合破坏指数。进而建立地震动峰值加速度（peak ground acceleration, PGA）与坝基累积滑移、坝顶相对位移、整体损伤指数3个单一指标和综合响应指标的对数概率地震需求模型。同时,结合各指标震害等级划分标准得到易损性曲线,对比研究近断层地震动的脉冲特性以及单一和综合响应指标对混凝土重力坝抗震性能的影响规律。研究结果表明,混凝土重力坝在遭遇近断层脉冲型地震动时发生轻微、中等、严重损伤的破坏概率均高于非脉冲型地震动,采用单一指标进行评价会导致某些PGA下高估重力坝抗震性能。而采用综合破坏指数作为性能指标来评价重力坝的震害概率和极限抗震能力更为合理。

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宋志强（1981—）,男,教授,博士,主要从事水工结构抗震研究。E-mail：
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李志龙（1984—）,男,高级工程师,博士研究生,主要从事水电及新能源发展研究。E-mail：

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李志龙（1984—）,男,高级工程师,博士研究生,主要从事水电及新能源发展研究。E-mail：

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李志龙（1984—）,男,高级工程师,博士研究生,主要从事水电及新能源发展研究。E-mail：

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motion intensities, figureFileSmall=8j39LQnmVMrpGR91uekKcA==, figureFileBig=mqkV0lFgYaijqMQHIEvBOQ==, tableContent=null), ArticleFig(id=1241802955167437359, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794072449454144, language=CN, label=图11, caption=不同地震动强度下重力坝破坏概率

注：L为坝基累积滑移；R为坝顶相对位移；M为整体损伤指数；D为综合破坏指数。

, figureFileSmall=8j39LQnmVMrpGR91uekKcA==, figureFileBig=mqkV0lFgYaijqMQHIEvBOQ==, tableContent=null), ArticleFig(id=1241802955314238011, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794072449454144, language=EN, label=Table 1, caption=

Selecting near-fault ground motion records and characteristic parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
地震动类型台站名称及分量编号RUP/kmPGA/gPGV/（m/s）PGV/PGA
脉冲型TCU050-EW19.490.1430.3680.26
TCU051-EW27.640.1570.5380.37
TCU056-EW310.480.1530.4220.24
TCU082-EW45.160.2210.5490.28
TCU046-EW516.740.1420.2900.20
TCU048-EW613.530.1190.3430.29
TCU102-EW71.490.3040.9170.30
TCU128-EW813.130.1440.6370.44
非脉冲型TCU071-EW95.800.5180.5230.10
TCU072-EW107.080.4680.7190.15
TCU078-EW118.200.4390.4020.09
TCU079-EW1210.970.5810.7050.11
TCU045-EW1318.860.4730.5000.11
TCU074-EW140.700.5960.7030.12
TCU076-EW152.740.3440.5180.15
TCU129-EW161.801.0100.4840.05
), ArticleFig(id=1241802955469427271, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794072449454144, language=CN, label=表1, caption=

选取近断层地震动记录及特征参数

, figureFileSmall=null, figureFileBig=null, tableContent=
地震动类型台站名称及分量编号RUP/kmPGA/gPGV/（m/s）PGV/PGA
脉冲型TCU050-EW19.490.1430.3680.26
TCU051-EW27.640.1570.5380.37
TCU056-EW310.480.1530.4220.24
TCU082-EW45.160.2210.5490.28
TCU046-EW516.740.1420.2900.20
TCU048-EW613.530.1190.3430.29
TCU102-EW71.490.3040.9170.30
TCU128-EW813.130.1440.6370.44
非脉冲型TCU071-EW95.800.5180.5230.10
TCU072-EW107.080.4680.7190.15
TCU078-EW118.200.4390.4020.09
TCU079-EW1210.970.5810.7050.11
TCU045-EW1318.860.4730.5000.11
TCU074-EW140.700.5960.7030.12
TCU076-EW152.740.3440.5180.15
TCU129-EW161.801.0100.4840.05
), ArticleFig(id=1241802955616227924, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794072449454144, language=EN, label=Table 2, caption=

Parameter table of concrete and bedrock material

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类型密度/（kg/m3）弹性模量/GPa泊松比抗压强度/MPa抗拉强度/MPa
C20240025.50.16713.41.54
C25240028.00.16716.71.78
基岩280012.00.2806.01.50
), ArticleFig(id=1241802955733668450, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794072449454144, language=CN, label=表2, caption=

混凝土、基岩材料参数表

, figureFileSmall=null, figureFileBig=null, tableContent=
类型密度/（kg/m3）弹性模量/GPa泊松比抗压强度/MPa抗拉强度/MPa
C20240025.50.16713.41.54
C25240028.00.16716.71.78
基岩280012.00.2806.01.50
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Criteria for categorizing damage levels of concrete gravity dams

, figureFileSmall=null, figureFileBig=null, tableContent=
震害等级轻微破坏中等破坏严重破坏
具体描述略加修复便可恢复正常运行有明显裂缝,局部渗漏,需检修后才可正常使用出现贯穿裂缝,渗漏严重,修复困难
坝基累积滑移L0~0.05dp0.05dp~0.20dp0.20dp~0.50dp
坝顶相对位移R0~0.035%0.035%~0.105%0.105%~0.154%
整体损伤指数M0≤M<0.150.15≤M<0.400.40≤M<0.73
综合破坏指数D0≤D<0.190.19≤D<0.510.51≤D<0.79
), ArticleFig(id=1241802956002103927, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794072449454144, language=CN, label=表3, caption=

混凝土重力坝震害等级划分标准

, figureFileSmall=null, figureFileBig=null, tableContent=
震害等级轻微破坏中等破坏严重破坏
具体描述略加修复便可恢复正常运行有明显裂缝,局部渗漏,需检修后才可正常使用出现贯穿裂缝,渗漏严重,修复困难
坝基累积滑移L0~0.05dp0.05dp~0.20dp0.20dp~0.50dp
坝顶相对位移R0~0.035%0.035%~0.105%0.105%~0.154%
整体损伤指数M0≤M<0.150.15≤M<0.400.40≤M<0.73
综合破坏指数D0≤D<0.190.19≤D<0.510.51≤D<0.79
), ArticleFig(id=1241802956257956485, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794072449454144, language=EN, label=Table 4, caption=

Constant weighting for a single response index

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地震动类型参数坝基滑移坝顶相对位移整体损伤指数
脉冲型复相关系数ρ0.63040.79730.7775
常权权重ω0.38440.30390.3117
非脉冲型复相关系数ρ0.93080.92350.7736
常权权重ω0.31140.31390.3747
), ArticleFig(id=1241802956350231179, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794072449454144, language=CN, label=表4, caption=

单一响应指标常权权重

, figureFileSmall=null, figureFileBig=null, tableContent=
地震动类型参数坝基滑移坝顶相对位移整体损伤指数
脉冲型复相关系数ρ0.63040.79730.7775
常权权重ω0.38440.30390.3117
非脉冲型复相关系数ρ0.93080.92350.7736
常权权重ω0.31140.31390.3747
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近断层地震作用下基于综合破坏指数的重力坝易损性分析
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李志龙 1, 2 , 刘云贺 1 , 张争 3 , 李香江 1 , 李闯 1 , 宋志强 1
地震工程与工程振动 | 研究论文 2025,45(5): 131-141
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地震工程与工程振动 | 研究论文 2025, 45(5): 131-141
近断层地震作用下基于综合破坏指数的重力坝易损性分析
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李志龙1, 2 , 刘云贺1, 张争3, 李香江1, 李闯1, 宋志强1
作者信息
  • 1.西安理工大学旱区水工程生态环境全国重点实验室,陕西西安710048
  • 2.国家能源集团西藏电力有限公司,西藏林芝860114
  • 3.中国电力工程顾问集团西北电力设计院有限公司,陕西西安710075

    • 李志龙（1984—）,男,高级工程师,博士研究生,主要从事水电及新能源发展研究。E-mail：

通讯作者:

宋志强（1981—）,男,教授,博士,主要从事水工结构抗震研究。E-mail：
Vulnerability analysis of gravity dams based on comprehensive damage index under near-fault earthquake action
Zhilong LI1, 2 , Yunhe LIU1, Zheng ZHANG3, Xiangjiang LI1, Chuang LI1, Zhiqiang SONG1
Affiliations
  • 1.State Key Laboratory of water Engineering Ecology and Environment in Arid Area, Xi’an University of Technology, Xi’an 710048, China
  • 2.CHN Energy Xizang Power Company Limited, Linzhi Xizang 860114, China
  • 3.Northwest Electric Power Design Institute Co., Ltd. of China Power Engineering Consulting Group, Xi’an 710075, China
出版时间: 2025-10-22 doi: 10.13197/j.eeed.2025.0513
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摘要
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近断层脉冲型地震动对混凝土重力坝抗震性能有重要影响,然而,目前对近断层地震动作用下混凝土重力坝的易损性研究较少,且均以单一响应指标为性能指标,难以全面表征重力坝的抗震性能。该文以某工程混凝土重力坝为例,建立坝体-地基整体塑性损伤模型。通过选取多条实测近断层脉冲型和非脉冲型地震动,依据功效系数法加变权模型的方式计算得到重力坝综合破坏指数。进而建立地震动峰值加速度（peak ground acceleration, PGA）与坝基累积滑移、坝顶相对位移、整体损伤指数3个单一指标和综合响应指标的对数概率地震需求模型。同时,结合各指标震害等级划分标准得到易损性曲线,对比研究近断层地震动的脉冲特性以及单一和综合响应指标对混凝土重力坝抗震性能的影响规律。研究结果表明,混凝土重力坝在遭遇近断层脉冲型地震动时发生轻微、中等、严重损伤的破坏概率均高于非脉冲型地震动,采用单一指标进行评价会导致某些PGA下高估重力坝抗震性能。而采用综合破坏指数作为性能指标来评价重力坝的震害概率和极限抗震能力更为合理。

近断层脉冲型地震动  /  混凝土重力坝  /  功效系数法  /  综合破坏指数  /  易损性分析

Existing studies have shown that near-fault impulsive ground motions have a significant impact on the seismic performance of concrete gravity dams. However, current research on the vulnerability of concrete gravity dams under near-fault ground motions remains limited, and most studies use a single response parameter as the performance indicator, which makes it difficult to comprehensively characterize the seismic performance of gravity dams. Taking a certain engineering concrete gravity dam as an example, this paper establishes a unified plastic damage model of the dam-foundation system. Multiple measured near-fault impulsive and non-impulsive ground motions are selected. Then, it calculates the comprehensive damage index of the gravity dam is calculated using the method of efficacy coefficient combined with the modified weighting model. A logarithmic probability seismic demand model is established for PGA (peak ground acceleration) and three single indices including accumulated base sliding, relative displacement of the dam crest, and overall damage index, as well as a comprehensive response index. By combining the criteria for dividing damage levels for each index, vulnerability curves are obtained. The paper compares the characteristics of near-fault ground motion pulses and the influence of single and comprehensive response indices on the seismic performance of concrete gravity dams. The results indicate that the probability of concrete gravity dams experiencing minor, moderate, and severe damage under near-fault impulsive ground motions is higher than that under non-impulsive ground motions. Evaluating seismic performance using a single index may lead to overestimation of the dam's seismic resistance under certain PGAs. Using a comprehensive damage index as the performance indicator for evaluating the probability of damage and ultimate seismic capacity of gravity dams is more reasonable.

near-fault impulsive ground motion  /  concrete gravity dam  /  efficacy coefficient method  /  comprehensive damage index  /  vulnerability analysis
李志龙, 刘云贺, 张争, 李香江, 李闯, 宋志强. 近断层地震作用下基于综合破坏指数的重力坝易损性分析. 地震工程与工程振动, 2025 , 45 (5) : 131 -141 . DOI: 10.13197/j.eeed.2025.0513
Zhilong LI, Yunhe LIU, Zheng ZHANG, Xiangjiang LI, Chuang LI, Zhiqiang SONG. Vulnerability analysis of gravity dams based on comprehensive damage index under near-fault earthquake action[J]. Earthquake Engineering and Engineering Dynamics, 2025 , 45 (5) : 131 -141 . DOI: 10.13197/j.eeed.2025.0513
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0　引言
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地震易损性分析是基于性能的抗震设计方法,基于地震易损性分析研究评价混凝土重力坝的抗震性能和极限抗震能力是目前大坝抗震研究的热点[1-5]。我国高坝大库建设主要集中在西部地区,坝址选择很难避让近断层区域,近断层脉冲型地震动短时间内的高能量输入,对坝体安全会产生重大影响[6-8]。因此,开展近断层脉冲型地震动作用下混凝土重力坝易损性分析研究具有重要意义。
研究近断层地震动对重力坝抗震性能的影响,是近年非常活跃的研究领域。HEBBOUCHE等[1]采用拉丁超立方的抽样方法研究了在近断层地震动下影响重力坝易损性的敏感参数。HUANG等[2]研究了近场地震动非一致输入对重力坝累计损伤效应的影响。ZHAI等[6,9]通过建立坝体-地基整体损伤模型,研究了脉冲型地震动作用下重力坝整体损伤演化规律。张社荣等[7]研究了具有方向性效应的近断层地震动对混凝土重力坝累积损伤的影响规律。结构地震易损性分析的关键问题是选取合理的破坏评价指标和震害等级划分标准。沈怀至[10]建立了坝基交界面非线性接触模型,以残余累积滑移为评价指标开展了重力坝易损性研究。ABDELHAMID等[11]提出以重力坝易损伤部位应力状态为评价指标,并通过分析给出了4级震害等级划分标准。王超等[12]提出基于整体损伤指数的重力坝破坏等级评价模型,并给出了5级震害等级划分标准。马智勇等[13]提出了基于位移响应指标和相应震害等级划分标准的重力坝易损性分析方法。上述学者在研究近断层地震动对重力坝的影响时只关注了重力坝某些单一响应特性,未系统地研究重力坝的整体抗震性能,以单一响应指标开展的重力坝易损性分析不足以反映坝体实际发生的多种破坏模式[3,14]。
本文以某实际工程混凝土重力坝为例,建立坝体-地基整体塑性损伤模型,选取多条实测近断层脉冲型和非脉冲型地震动,采用增量动力分析（incremental dynamic analysis, IDA）计算方法,以3个单一响应指标为基础,先采用功效系数法得到各指标常权权重和功效系数,再应用变权模型计算坝体的综合破坏指数,最后以综合破坏指数为评价指标,对比研究近断层地震动的脉冲特性和综合指标对重力坝抗震性能的影响。本文为混凝土重力坝抗震性能的评价提供更为全面且符合实际的分析模型和方法。
1　易损性分析方法及综合破坏指数计算原理
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1.1　基于IDA的易损性分析方法
易损性分析是结构抗震性能研究的延续,其可以预测结构在不同强度地震下发生各级震害的超越概率。IDA法是一种参数化分析方法[15],通过调节每条地震动的参数得到一组不同强度的地震动,再采用这组地震动分别对结构进行非线性动力时程分析,最后绘制以性能参数（DM）为纵轴,相应地震动参数（IM）为横轴的曲线,即为IDA曲线。本文基于IDA法开展混凝土重力坝的易损性研究,地震易损性通常采用易损性曲线表示。
根据相关研究[4,13],结构DM和IM的指数关系为
式中,a和b为回归拟合系数,对式（1）两边取对数,得到结构的概率地震需求模型如式（2）所示：
在易损性分析时,一般假设地震易损性服从对数正态分布,可得到结构超过相应性能水准（LS）达到各震害等级的累计概率如式（3）所示：
式中：FLS（xPGA）为某一性能水准下的地震易损性函数；xPGA为指定地震动强度；Φ[•]为标准正态累积分布函数；μ为结构响应指标的对数标准差,按式（4）计算,得
式中,n为式（2）线性回归数据点个数。将式（2）和式（4）代入式（3）,得到易损性曲线表达式为
将IDA计算分析得到的指标代入式（5）,即可得到此响应指标下混凝土重力坝的易损性曲线。
1.2　综合破坏指数计算原理
以单一破坏指标评价坝体的整体破坏情况是不完善的[3,14]。本文在计算多个单一响应指标的基础上,采用功效系数法加变权模型的方式,得到综合破坏指数,以便更加全面、合理地评估混凝土重力坝的破坏状态。
功效系数法[16-17]是多目标综合评价广泛采用的方法。首先,将各单一响应指标采用归一化的方法分别转化为无量纲的相对数,即功效分数dijk,按式（6）计算：
再将dijk采用加权平均的方式计算总的功效系数,即为综合破坏指数Dij,按式（7）计算：
式中：xijk为第i条地震动第j次调幅计算的第k项指标；为第k项指标不允许出现的最坏值；为第k项指标可能达到的最好值；p为选取指标个数；ωk为第k项指标的常权权重,按式（8）、式（9）计算,得
式中：ρk为复相关系数,它的大小反映某项指标k与其余指标的线性相关水平,即指标k能被其余指标线性表达的能力,ρk越大,则指标k权重越小；SSres为残差平方和；SStot为总离差平方和。
在实际分析过程中,各指标受不同地震动强度的影响不同,指标的权重如果一直维持不变会对坝体破坏等级评价产生重要影响,因此引入变权模型。参考刘肖军等[3]的研究,采用均衡函数的变权公式,如式（10）所示：
式中：α为变权公式分类参数,取α=1.5[18]；cijk为第i条地震动第j次调幅计算的第k项指标的标准转化量,如式（11）所示：
式中：m为xijk所在大坝震害评价等级（1,2,3）；和分别为指标k所处等级区间的最大值和最小值。
将式（8）、式（10）代入式（9）,再将式（6）、式（9）代入式（7）,即得到综合破坏指数计算公式为
2　近断层地震动的选取
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在采用IDA法进行重力坝易损性分析前,需选取大量地震动记录作为输入地震波。本文为确保所选取的地震动更好地体现地震具有的不确定性和随机性,从太平洋地震工程研究中心（Pacific Earthquake Engineering Research Center, PEER）数据库选取16条实测地震动,其中脉冲型与非脉冲型各8条,各条地震动特征参数统计整理见表1。近断层地震动选取的规则是[19]：断层距（rupture distance, RUP）<20 km；脉冲型地震动的选取规则是：峰值速度比峰值加速度（PGV/PGA）>0.2,峰值加速度（PGA）>0.1 g。
实测地震动的持时很长,但实际对结构产生影响的持时较短,在提高计算效率且不影响计算结果的前提下,本文截取每条地震动能量在5%~95%的时段进行非线性动力计算。采用IDA法分析时,每条地震动峰值加速度调幅范围为0.1~0.8 g,调幅步长0.1 g,水平向加速度选用实测地震动东西向（EW）分量,竖向加速度选用垂直向（V）分量。
台站TCU050（脉冲型）和台站TCU074（非脉冲型）的速度、位移时程见图1。由图可知,脉冲型地震动速度和位移在短时间内会急剧增大,具有明显的双向速度脉冲效应和位移脉冲效应,图中所示脉冲型地震动的峰值速度PGV是非脉冲型地震动PGV的2.13倍,峰值位移PGD是非脉冲型地震动的11.62倍。由表1选取的实测地震动记录均调幅为0.1 g后的加速度反应谱及其均值反应谱见图2。由图可知,在高频段脉冲型与非脉冲型地震动的平均加速度谱值较为接近,在中、低频段脉冲型地震动的反应谱值更大,脉冲型地震动具有更宽的加速度反应谱敏感区。
3　混凝土重力坝易损性分析
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3.1　坝体-地基有限元模型及计算参数
以某工程混凝土重力坝的典型非溢流坝段为例,建立有限元模型开展动力非线性计算。坝高为85 m,坝顶宽度为14 m,坝体上游正常蓄水位为82.6 m,下游水位为29.1 m。地基范围自坝踵、坝趾和坝底分别向坝体上游、下游和底部延伸2倍坝高170 m。坝主体采用C20混凝土,上游坝面采用C25混凝土。为更好地反映重力坝地震损伤破坏情况,坝体和地基都采用塑性损伤模型（concrete damage plasticity model, CDP）[20],基岩抗拉强度通过M-C准则中的ft=2c•cosφ/（1+sinφ）推求,具体参数见表2。坝体和基岩接触面采用考虑黏聚力的库伦摩擦模型。坝体Rayleigh阻尼系数根据计算得到的前两阶频率计算,阻尼比取10%。模型整体采用平面应变四边形单元CPE4划分,共划分单元6685个,结点6921个。模型网格划分见图3。
采用有限元计算软件ABAQUS进行动力时程分析,计算荷载考虑模型自重、上下游水压力、地震作用和动水压力,动水压力采用Westergard附加质量模型模拟,地震作用采用黏弹性边界波动输入,地震波在底部折半,输入方向为从底部垂直入射。
以选取的16条地震动为依据,按照IDA法调幅为0.1~0.8 g,共得到128条地震动即128个计算工况,开展混凝土重力坝的非线性响应分析。
3.2　单一响应指标选取及震害等级划分标准
在结构易损性分析前,需要选取合适的响应指标评价坝体的震害情况。沈怀至等[4]考虑坝体-地基系统材料参数的不确定性,建立了以坝体和坝基交界面的滑动位移为评价指标的重力坝易损性分析方法。王超等[12]提出基于整体损伤指数的重力坝破坏等级评价模型,并以此进行了重力坝易损性分析。马智勇等[13]、刘金芳等[21]以坝顶相对位移为抗震性能指标,建立了基于坝顶相对位移的重力坝地震易损性分析方法。刘肖军等[3]、姚倩茹等[14]考虑不同的响应指标,基于综合破坏指数开展了重力坝的易损性研究。本文基于众多学者的研究,选取坝基累积滑移、坝顶相对坝踵的顺河向位移和整体损伤指数3个单一响应指标。本文划分混凝土重力坝的震害等级为轻微破坏、中等破坏和严重破坏3级,划分标准见表3。
表3中坝基累积滑移L为动力计算结束时坝踵单元与接触的地基单元的顺河向残余相对位移。坝顶相对位移R为坝顶相对坝踵的顺河向位移最大值占坝高的百分比。整体损伤指数M采用考虑坝体局部损伤区域影响权重的方式加权计算[12],具体计算方法为
式中：Mi为损伤区域i的局部损伤指数；tij为区域i第j个单元的损伤因子；Sij为单元面积；αi为损伤区域i的权重系数,当从上游迎水面开始破坏时,取1.0,其他情况取0.8；等于裂缝开裂长度li与其所在路径长度Li的比值。
在得到局部损伤指数后,认为损伤区域高程越高,则对大坝整体结构影响越小,定义整体损伤指数M,得
式中：N为大坝损伤区域数量；λi为损伤区域i的局部损伤权重系数；H为坝高,hi为损伤区域i的中心高度；d为损伤指标中等破坏下限值。
3.3　基于单一响应指标的易损性分析
台站TCU050（脉冲型）和TCU074（非脉冲型）部分强度下的坝体损伤图,见图4和图5。由图可知, PGA为0.3 g时,脉冲型地震动作用下坝体下游折坡处已经出现轻微损伤,非脉冲型地震动作用下坝体基本无损伤；PGA为0.4 g时,脉冲型地震动作用下坝体下游折坡处损伤裂缝扩展,接近贯通坝体,非脉冲型地震动作用下坝体才出现轻微损伤。综合对比各强度下重力坝损伤区域,脉冲型地震动相比非脉冲型地震动作用下重力坝会出现更严重的损伤破坏,这是由于脉冲型地震动的速度脉冲效应在短时间内给坝体-地基系统输入了足够大的能量,使得结构体系能量无法有效耗散,导致坝体出现大面积损伤。但在PGA强度足够高时,无论哪种地震动坝体都会出现严重破坏,见图4（d）和图5（d）,在0.6 g地震动下,2个工况坝体都已出现大面积贯穿裂缝,修复难度大,都达到严重破坏等级。
在IDA分析计算完成后,需对各工况单一响应指标进行对数线性回归拟合,建立概率地震需求模型。将各工况坝基累积滑移、坝顶相对位移和整体损伤指数计算结果分别与相应PGA转化到对数空间内,在对数坐标系下基于最小二乘法进行一元线性回归拟合,见图6和图7,分别给出了脉冲型地震动和非脉冲型地震动作用下各单一响应指标概率地震需求模型线性拟合结果,图中横坐标“ln（PGA）”中PGA的单位为“m/s2”,R2为线性回归决定系数,R2越大,线性回归拟合越好。由图可知,非脉冲型地震动坝基滑移拟合R2最小,为0.763,其余各指标拟合R2都在0.8~0.9之间,拟合情况较好。
将图6、图7概率地震需求模型和表3震害等级划分标准代入式（5）,即可得到脉冲型地震动和非脉冲型地震动各单一响应指标、各震害等级下的易损性曲线,见图8。由图可知,脉冲型地震动易损性曲线在各震害等级下均高于非脉冲型地震动易损性曲线,在同一地震动强度下脉冲型地震动发生各级震害的概率更高。
以坝基滑移为评价指标时,2种地震动下轻微损伤的易损性曲线大致相同,发生中等、严重损伤的概率都是脉冲型地震动大,当大坝遭遇PGA为0.4 g地震作用时,非脉冲型地震作用下发生中等、严重损伤的概率分别为68.4%、15.3%,而在脉冲型地震作用下发生中等、严重损伤的概率分别提高到95.8%、44.8%,说明在重力坝遭遇近断层脉冲型地震且强度大于0.4 g时,坝体大概率会发生中等破坏,见图8（a）。以坝顶相对位移为评价指标时,2种地震动下轻微损伤的易损性曲线基本一致,发生中等、严重损伤的概率都是脉冲型地震动略大,当大坝遭遇PGA为0.4 g地震作用时,脉冲型地震相比非脉冲型地震作用下发生中等、严重损伤的概率分别由57.5%、27.3%提高到73.7%、42.4%,见图8（b）。以整体损伤指数为评价指标时,脉冲型地震动下发生轻微、中等、严重损伤的概率都比非脉冲型地震动大,但在一定强度后2种地震动发生各级损伤的概率会趋于一致,当大坝遭遇PGA为0.4 g地震作用时,脉冲型地震相比非脉冲型地震作用下发生中等、严重损伤的概率分别由53.7%、2.7%提高到69.5%、19.9%,见图8（c）。
综上可以看出,当重力坝遭遇同一强度地震时,采用坝基滑移和坝顶相对位移为评价指标会偏于保守,采用整体损伤指数为评价指标又偏于危险,不同评价指标下重力坝发生各级破坏的概率均不同,以单一响应指标进行坝体的震害评价不够精确、全面。
3.4　基于综合破坏指数的易损性分析
本文采用变权功效系数法可以综合考虑多项指标对坝体的震害等级评价的贡献。根据重力坝所有动力工况下的响应结果,计算各指标的复相关系数代入式（8）,得到脉冲型地震动和非脉冲型地震动的坝基滑移、坝顶相对位移和整体损伤指数的常权权重见表4。再将常权权重代入式（9）即可得到各工况下各指标的变权权重,以此可计算得到各工况的综合破坏指数。脉冲型地震动和非脉冲型地震动综合破坏指数概率地震需求模型线性拟合结果见图9。由表4可知,在脉冲型地震动下坝基滑移的常权权重最大,为0.3844；非脉冲型地震动下整体损伤指数的常权权重最大,为0.3747。
将图9的概率地震需求模型和表3中综合破坏指数震害等级划分标准代入式（5）,即可得到脉冲型地震动和非脉冲型地震动在综合破坏指数下的易损性曲线见图10。由图可知,脉冲型地震动关于综合破坏指数的易损性曲线在各震害等级下均高于非脉冲型地震动易损性曲线,在同一地震动强度下以综合破坏指数为评价指标时,脉冲型地震动发生各级震害的超越概率更大,以综合破坏指数为评价指标开展混凝土重力坝的易损性分析更加全面客观。
以脉冲型地震动为例,在重力坝遭遇PGA为0.2 g的地震时,4种评价指标下发生轻微损伤的概率分别为94.2%、70.1%、41.7%、70.5%。可以看出,以坝基滑移为评价指标时0.2 g地震下坝体基本至少都会发生轻微损伤,以整体损伤指数为评价指标只有不到一半的概率会发生轻微损伤,而变权模型通过降低坝基滑移的权重和增大整体损伤指数的权重,得到的坝体发生轻微损伤的概率更加合理。在重力坝遭遇PGA为0.4 g的地震时,综合破坏指数下发生中等、严重损伤的概率分别为80.9%、36.3%,结合第3.3节可以看出,变权模型通过调节（增强或削弱）各单一指标的权重,得到的坝体发生中等、严重损伤的概率能够不受主观因素影响,更加全面准确。
本文混凝土重力坝地震安评后的设计地震动强度和校核地震动强度分别为0.22、0.34 g,通过对图10中易损性曲线进行插值,可以得到大坝在遭遇设计和校核地震时不同评价指标的破坏超越概率见图11。由图可知,无论哪种评价指标下,重力坝以近断层脉冲型地震动为输入波时达到轻微、中等和严重损伤的概率都比非脉冲型地震动作用下的概率高,以综合破坏指数为评价指标可以平衡各单一指标的不足,得到更贴合实际的破坏概率。
在脉冲型地震动下,坝体遭遇设计地震时,有接近80%的概率会发生轻微损伤,发生中等损伤不到15%,发生严重损伤的概率几乎为0；在遭遇校核地震时,有97.1%的概率会发生轻微损伤,发生中等损伤的概率超过60%,发生严重损伤的概率也有17.4%。在非脉冲型地震动下,坝体遭遇设计地震时,只有接近60%的概率会发生轻微损伤,发生中等损伤的概率只有6%,发生严重损伤的概率几乎为0；在遭遇校核地震时,有92.0%的概率会发生轻微损伤,发生中等损伤的概率不到40%,发生严重损伤的概率只有6.7%。
可以看出,由设计地震到校核地震的各震害等级破坏概率的增幅表现为近断层脉冲型地震动大于非脉冲型地震动,说明只采用非脉冲地震动会高估大坝的极限抗震能力,此工程重力坝在非脉冲型地震动下很难发生严重破坏,而在脉冲型地震动下有接近20%的概率会发生严重破坏。
4　结论
收起
本文以选取的3个重力坝震损单一响应指标为基础,采用功效系数法加变权模型的方式计算综合破坏指数,最后基于综合破坏指数研究了地震动脉冲特性对混凝土重力坝抗震性能的影响规律,得到如下主要结论：
1）采用综合破坏指数进行混凝土重力坝易损性评价,可以通过调节各单一响应指标在评价不同强度地震下的权重,更加全面准确地表征坝体的破坏模式。
2）混凝土重力坝在遭遇近断层脉冲型地震动时发生轻微、中等、严重损伤的破坏概率均高于非脉冲型地震动,此工程重力坝由设计地震到校核地震的各震害等级破坏概率的增幅表现为近断层脉冲型地震动大于非脉冲型地震动。
基金
收起
  • 国家自然科学基金重点项目(52039008)
  • 陕西省自然科学基础研究计划面上项目(2022JM-276)
  • 陕西省教育厅青年创新团队科研计划项目(22JP052)
文献
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2025年第45卷第5期
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doi: 10.13197/j.eeed.2025.0513
  • 接收时间：2024-05-07
  • 首发时间：2026-03-20
  • 出版时间：2025-10-22
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  • 收稿日期：2024-05-07
  • 修回日期：2024-09-10
基金
国家自然科学基金重点项目(52039008)
陕西省自然科学基础研究计划面上项目(2022JM-276)
陕西省教育厅青年创新团队科研计划项目(22JP052)
作者信息
    1.西安理工大学旱区水工程生态环境全国重点实验室,陕西西安710048
    2.国家能源集团西藏电力有限公司,西藏林芝860114
    3.中国电力工程顾问集团西北电力设计院有限公司,陕西西安710075

通讯作者:

宋志强（1981—）,男,教授,博士,主要从事水工结构抗震研究。E-mail：
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