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Article(id=1245390012439707885, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390004252426256, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0318, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1706198400000, receivedDateStr=2024-01-26, revisedDate=1710518400000, revisedDateStr=2024-03-16, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853717193, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853717193, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853717193, creator=13701087609, updateTime=1774853717193, updator=13701087609, issue=Issue{id=1245390004252426256, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='3', pageStart='1', pageEnd='230', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774853715241, creator=13701087609, updateTime=1774854338522, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245392618545332491, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390004252426256, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245392618545332492, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390004252426256, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=182, endPage=189, ext={EN=ArticleExt(id=1245390012813000962, articleId=1245390012439707885, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Seismic vulnerability and average loss ratio analysis of mountainous tunnels based on Ms8.0 Wenchuan earthquake, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Based on the seismic damage data of Wenchuan earthquake, the seismic vulnerability model of entirety and different sections of mountainous tunnel is obtained by regression analysis. The peak ground acceleration (PGA) was selected as the ground motion parameter and the lognormal distribution was selected as the vulnerability model, and the seismic vulnerability curves of the tunnel structure of entirety and different sections (entrance shallow burial section, entrance transition section, ordinary section, fractured section) were obtained by the maximum likelihood estimation, and the vulnerability characteristics of different section and the whole tunnel were compared and analyzed. Under the condition of slight damage, the seismic vulnerability of the entrance shallow burial section is higher than that of other section. With the increase of the degree of damage, the seismic vulnerability of the fractured section is gradually higher than that of other sections of the tunnel. The average loss rate model of the tunnel was established by combining the loss ratio of tunnel structure in a specific failure state. The tunnel vulnerability models and average loss ratio model established in this paper can be used to evaluate the seismic loss rapidly in the event of similar earthquakes in the future.

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基于汶川地震震害资料，通过回归分析得到了山区隧道结构整体与各部分的地震易损性模型。选择峰值地面加速度（peak ground acceleration，PGA）作为地震动参数，以对数正态分布函数作为易损性模型，利用极大似然估计得到隧道结构整体及各部分（洞口浅埋段、洞口过渡段、普通段、断层破碎段）的地震易损性曲线，对比分析了隧道整体及各部分的地震易损性特点并进行了探讨。结果表明：轻微破坏条件下，洞口浅埋段的地震易损性要高于其他部分。随着破坏程度的增加，断层破碎带段的地震易损性逐渐高于隧道其他部分。根据隧道结构特定破坏等级的损失比，建立了隧道的平均损失率模型。依据文中建立的隧道易损性模型及平均损失率模型可以在将来发生类似地震时快速地进行地震损失评估。

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李廷辉（1992—），男，讲师，博士，主要从事生命线工程抗震及易损性研究。E-mail：
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孙路（1979—），女，副教授，博士，主要从事生命线工程抗震研究。E-mail：

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孙路（1979—），女，副教授，博士，主要从事生命线工程抗震研究。E-mail：

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孙路（1979—），女，副教授，博士，主要从事生命线工程抗震研究。E-mail：

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label=Fig. 1, caption=Typical tunnel seismic damages, figureFileSmall=Pf1GsShD9bW+BV5LXSFGwA==, figureFileBig=O7ZimU15UWkJzackMZmC+w==, tableContent=null), ArticleFig(id=1245390018349482677, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=图1, caption=典型隧道震害, figureFileSmall=Pf1GsShD9bW+BV5LXSFGwA==, figureFileBig=O7ZimU15UWkJzackMZmC+w==, tableContent=null), ArticleFig(id=1245390018643083978, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Fig. 2, caption=Ratio of different damage grades of tunnels, figureFileSmall=rmM/BYQAE21it0LApPukfg==, figureFileBig=SIh8ggPhbI0KqAozx0p7AQ==, tableContent=null), ArticleFig(id=1245390018760524496, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=图2, caption=隧道不同破坏等级占比, figureFileSmall=rmM/BYQAE21it0LApPukfg==, figureFileBig=SIh8ggPhbI0KqAozx0p7AQ==, tableContent=null), ArticleFig(id=1245390018886353624, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Fig. 3, caption=Tunnel seismic vulnerability curves based on Wenchuan earthquake, figureFileSmall=Mywxcp2Kq35KyEQVdcgGlA==, figureFileBig=ubwJD9KpKhFDvGjLiGPoUg==, tableContent=null), ArticleFig(id=1245390018995405539, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=图3, caption=基于汶川地震的隧道易损性曲线, figureFileSmall=Mywxcp2Kq35KyEQVdcgGlA==, figureFileBig=ubwJD9KpKhFDvGjLiGPoUg==, tableContent=null), ArticleFig(id=1245390019096068843, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Fig. 4, caption=Comparison of seismic vulnerability curves of tunnel sections, figureFileSmall=5PIu7XokogcnToIOfTYl8Q==, figureFileBig=nbcpXv74RB+IH1EgGKxeDQ==, tableContent=null), ArticleFig(id=1245390019326755574, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=图4, caption=隧道各部分地震易损性曲线对比, figureFileSmall=5PIu7XokogcnToIOfTYl8Q==, figureFileBig=nbcpXv74RB+IH1EgGKxeDQ==, tableContent=null), ArticleFig(id=1245390019440001788, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Fig. 5, caption=Average loss ratio of tunnels, figureFileSmall=GAUzIs2Bn3avwKn33VvpFg==, figureFileBig=tQJzeWkj5SZmbVbMETjypw==, tableContent=null), ArticleFig(id=1245390019519693570, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=图5, caption=隧道平均损失率, figureFileSmall=GAUzIs2Bn3avwKn33VvpFg==, figureFileBig=tQJzeWkj5SZmbVbMETjypw==, tableContent=null), ArticleFig(id=1245390019637134092, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Table 1, caption=

Seismic damage classification and characteristics of tunnels

, figureFileSmall=null, figureFileBig=null, tableContent=
破坏等级震害特征
基本完好无明显破坏
轻微破坏混凝土剥落，路面渗水，衬砌渗水，施工缝开裂，路面开裂（裂纹清晰，有一定走向；不能确定裂纹方向，呈片状或网状）
中等破坏混凝土掉块，衬砌开裂（裂纹清晰，有一定走向；不能确定裂纹方向，呈片状或网状）
严重破坏衬砌错台，二次衬砌垮塌，仰拱错台，仰拱隆起
毁坏隧道垮塌
), ArticleFig(id=1245390019741991699, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=表1, caption=

隧道震害分级及震害特征

, figureFileSmall=null, figureFileBig=null, tableContent=
破坏等级震害特征
基本完好无明显破坏
轻微破坏混凝土剥落，路面渗水，衬砌渗水，施工缝开裂，路面开裂（裂纹清晰，有一定走向；不能确定裂纹方向，呈片状或网状）
中等破坏混凝土掉块，衬砌开裂（裂纹清晰，有一定走向；不能确定裂纹方向，呈片状或网状）
严重破坏衬砌错台，二次衬砌垮塌，仰拱错台，仰拱隆起
毁坏隧道垮塌
), ArticleFig(id=1245390019842654998, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Table 2, caption=

Regression coefficient of PGA attenuation relation

, figureFileSmall=null, figureFileBig=null, tableContent=
系数N-SE-WU-D
C14.7874.7184.844
C2–1.314–1.284–1.446
δ0.2890.2860.303
), ArticleFig(id=1245390019989455646, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=表2, caption=

PGA衰减关系回归系数

, figureFileSmall=null, figureFileBig=null, tableContent=
系数N-SE-WU-D
C14.7874.7184.844
C2–1.314–1.284–1.446
δ0.2890.2860.303
), ArticleFig(id=1245390020094313253, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Table 3, caption=

Seismic damage matrix of tunnel entire samples

, figureFileSmall=null, figureFileBig=null, tableContent=
序号PGA/g破坏等级
基本完好轻微破坏中等破坏严重破坏毁坏
10.38911100
20.66611111
………
), ArticleFig(id=1245390020186587945, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=表3, caption=

隧道整体样本震害矩阵

, figureFileSmall=null, figureFileBig=null, tableContent=
序号PGA/g破坏等级
基本完好轻微破坏中等破坏严重破坏毁坏
10.38911100
20.66611111
………
), ArticleFig(id=1245390020320805684, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Table 4, caption=

Seismic damage matrix of tunnel entrance shallow burial section samples

, figureFileSmall=null, figureFileBig=null, tableContent=
序号PGA/g破坏等级
基本完好轻微破坏中等破坏严重破坏毁坏
10.38911000
20.66611110
………
), ArticleFig(id=1245390020434051898, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=表4, caption=

隧道洞口浅埋段样本震害矩阵

, figureFileSmall=null, figureFileBig=null, tableContent=
序号PGA/g破坏等级
基本完好轻微破坏中等破坏严重破坏毁坏
10.38911000
20.66611110
………
), ArticleFig(id=1245390020526326594, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Table 5, caption=

Parameter estimation values of the vulnerability function

, figureFileSmall=null, figureFileBig=null, tableContent=
参数轻微破坏中等破坏严重破坏毁坏
均值0.48021.04841.33962.6498
标准差1.01960.73860.48570.7094
), ArticleFig(id=1245390020639572811, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=表5, caption=

易损性函数的参数估计值

, figureFileSmall=null, figureFileBig=null, tableContent=
参数轻微破坏中等破坏严重破坏毁坏
均值0.48021.04841.33962.6498
标准差1.01960.73860.48570.7094
), ArticleFig(id=1245390020752819027, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Table 6, caption=

Parameter estimation values of the vulnerability function of entrance shallow burial section

, figureFileSmall=null, figureFileBig=null, tableContent=
参数轻微破坏中等破坏严重破坏
均值0.84771.15921.3154
标准差0.96560.26000.2562
), ArticleFig(id=1245390020845093721, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=表6, caption=

洞口浅埋段易损性函数的参数估计值

, figureFileSmall=null, figureFileBig=null, tableContent=
参数轻微破坏中等破坏严重破坏
均值0.84771.15921.3154
标准差0.96560.26000.2562
), ArticleFig(id=1245390020941562724, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Table 7, caption=

Parameter estimation values of the vulnerability function of entrance transition section

, figureFileSmall=null, figureFileBig=null, tableContent=
参数轻微破坏中等破坏严重破坏
均值1.41811.28571.3325
标准差1.31110.16360.1619
), ArticleFig(id=1245390021025448808, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=表7, caption=

洞口过渡段易损性函数的参数估计值

, figureFileSmall=null, figureFileBig=null, tableContent=
参数轻微破坏中等破坏严重破坏
均值1.41811.28571.3325
标准差1.31110.16360.1619
), ArticleFig(id=1245390021100946285, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Table 8, caption=

Parameter estimation values of the vulnerability function of ordinary section

, figureFileSmall=null, figureFileBig=null, tableContent=
参数轻微破坏中等破坏严重破坏
均值1.67501.37211.4153
标准差1.07410.17010.2083
), ArticleFig(id=1245390021193220980, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=表8, caption=

普通段易损性函数的参数估计值

, figureFileSmall=null, figureFileBig=null, tableContent=
参数轻微破坏中等破坏严重破坏
均值1.67501.37211.4153
标准差1.07410.17010.2083
), ArticleFig(id=1245390021293884282, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Table 9, caption=

Parameter estimation values of the vulnerability function of fault fractured section

, figureFileSmall=null, figureFileBig=null, tableContent=
参数轻微破坏中等破坏严重破坏毁坏
均值1.09921.50571.71272.6498
标准差1.01960.73860.48570.7094
), ArticleFig(id=1245390021398741888, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=表9, caption=

断层破碎带段易损性函数的参数估计值

, figureFileSmall=null, figureFileBig=null, tableContent=
参数轻微破坏中等破坏严重破坏毁坏
均值1.09921.50571.71272.6498
标准差1.01960.73860.48570.7094
), ArticleFig(id=1245390021495210887, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=EN, label=Table 10, caption=

Damage loss ratio of highway system engineering structure

, figureFileSmall=null, figureFileBig=null, tableContent=
损失比破坏等级
基本完好轻微破坏中等破坏严重破坏毁坏
范围0~1011~2021~4041~7071~100
中位值516315686
), ArticleFig(id=1245390021587485579, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012439707885, language=CN, label=表10, caption=

公路系统工程结构破坏损失比

, figureFileSmall=null, figureFileBig=null, tableContent=
损失比破坏等级
基本完好轻微破坏中等破坏严重破坏毁坏
范围0~1011~2021~4041~7071~100
中位值516315686
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汶川Ms8.0地震隧道易损性及平均损失率分析
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孙路 1, 2 , 李廷辉 3, 4, 5 , 郭霞 6
地震工程与工程振动 | 2024,44(3): 182-189
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地震工程与工程振动 | 2024, 44(3): 182-189
汶川Ms8.0地震隧道易损性及平均损失率分析
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孙路1, 2 , 李廷辉3, 4, 5 , 郭霞6
作者信息
  • 1.湖州职业技术学院 建筑工程学院，浙江 湖州 313000
  • 2.湖州市绿色建筑技术重点实验室，浙江 湖州 313000
  • 3.东北石油大学 土木建筑工程学院，黑龙江 大庆 163318
  • 4.黑龙江省寒区新能源热利用及防灾减灾重点实验室，黑龙江 大庆 163318
  • 5.黑龙江省教育厅防灾减灾及防护工程重点实验室，黑龙江 大庆 163318
  • 6.核工业湖州勘测规划设计研究院股份有限公司，浙江 湖州 313000

    • 孙路（1979—），女，副教授，博士，主要从事生命线工程抗震研究。E-mail：

通讯作者:

李廷辉（1992—），男，讲师，博士，主要从事生命线工程抗震及易损性研究。E-mail：
Seismic vulnerability and average loss ratio analysis of mountainous tunnels based on Ms8.0 Wenchuan earthquake
Lu SUN1, 2 , Tinghui LI3, 4, 5 , Xia GUO6
Affiliations
  • 1.School of Architectural Engineering, Huzhou Vocational & Technical College, Huzhou 313000, China
  • 2.Huzhou Key Laboratory of Green Building Technology, Huzhou 313000, China
  • 3.School of Civil Engineering and Architecture, Northeast Petroleum University, Daqing 163318, China
  • 4.Heilongjiang Provincial Key Laboratory of Thermal Utilization and Disaster Reduction of New Energy in Cold Regions, Daqing 163318, China
  • 5.Heilongjiang Key Laboratory of Disaster Prevention, Mitigation and Protection Engineering, Daqing 163318, China
  • 6.Nuclear Industry Huzhou Survey Planning & Design Institute Co., Ltd., Huzhou 313000, China
doi: 10.13197/j.eeed.2024.0318
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摘要
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基于汶川地震震害资料，通过回归分析得到了山区隧道结构整体与各部分的地震易损性模型。选择峰值地面加速度（peak ground acceleration，PGA）作为地震动参数，以对数正态分布函数作为易损性模型，利用极大似然估计得到隧道结构整体及各部分（洞口浅埋段、洞口过渡段、普通段、断层破碎段）的地震易损性曲线，对比分析了隧道整体及各部分的地震易损性特点并进行了探讨。结果表明：轻微破坏条件下，洞口浅埋段的地震易损性要高于其他部分。随着破坏程度的增加，断层破碎带段的地震易损性逐渐高于隧道其他部分。根据隧道结构特定破坏等级的损失比，建立了隧道的平均损失率模型。依据文中建立的隧道易损性模型及平均损失率模型可以在将来发生类似地震时快速地进行地震损失评估。

山区隧道  /  易损性模型  /  平均损失率  /  损失比

Based on the seismic damage data of Wenchuan earthquake, the seismic vulnerability model of entirety and different sections of mountainous tunnel is obtained by regression analysis. The peak ground acceleration (PGA) was selected as the ground motion parameter and the lognormal distribution was selected as the vulnerability model, and the seismic vulnerability curves of the tunnel structure of entirety and different sections (entrance shallow burial section, entrance transition section, ordinary section, fractured section) were obtained by the maximum likelihood estimation, and the vulnerability characteristics of different section and the whole tunnel were compared and analyzed. Under the condition of slight damage, the seismic vulnerability of the entrance shallow burial section is higher than that of other section. With the increase of the degree of damage, the seismic vulnerability of the fractured section is gradually higher than that of other sections of the tunnel. The average loss rate model of the tunnel was established by combining the loss ratio of tunnel structure in a specific failure state. The tunnel vulnerability models and average loss ratio model established in this paper can be used to evaluate the seismic loss rapidly in the event of similar earthquakes in the future.

mountainous tunnel  /  vulnerability model  /  average loss ratio  /  loss rate
孙路, 李廷辉, 郭霞. 汶川Ms8.0地震隧道易损性及平均损失率分析. 地震工程与工程振动, 2024 , 44 (3) : 182 -189 . DOI: 10.13197/j.eeed.2024.0318
Lu SUN, Tinghui LI, Xia GUO. Seismic vulnerability and average loss ratio analysis of mountainous tunnels based on Ms8.0 Wenchuan earthquake[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (3) : 182 -189 . DOI: 10.13197/j.eeed.2024.0318
正文
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0　引言
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对于山区交通系统而言，隧道与桥梁是最为重要的组成部分。例如四川棉广高速，其桥隧比高达62.25%，四川汶马高速，其桥隧比高达86%，而对于川藏铁路来讲，其桥隧比更是高达95.8%，其中，桥梁占比11.33%，隧道占比84.43%，可以说沿线全是由桥隧组成的，这在全世界都实属罕见。正是因为我国山区面积占全国土地面积的2/3以上的特点，造成了西部山区高速公路沿线道路占比较小的现状，而这些地区往往又是地震动活跃地区，在过去的十多年中，就相继发生了几次破坏性大地震，如2008年的汶川8.0级地震、2010年玉树7.1级地震以及2013年芦山7.0级地震等，隧道地震安全不容忽视。
隧道作为一种地下结构，长期以来一直被认为有能力在地震中维持较小的破坏。然而，历史震害表明这种想法是有偏颇的。在某些条件下，隧道的地震损伤程度也会很重。WANG等[1]对集集地震中的山区隧道进行了调查，调查结果显示许多隧道遭受了不同程度的严重破坏，57条隧道中有49条受损，且研究发现隧道的破坏程度与隧道的地质条件和结构布置有关，如穿越断层带的隧道一定会遭受破坏。ASAKURA等[2]收集了1995年兵库县南部地震中受损隧道的资料，研究了山地隧道的地震反应，并对隧道的地震损伤进行了研究，结果表明当地震规模较大时，隧道附近有地震断层或有特殊条件时，隧道有可能发生破坏。关于隧道的地震易损性，国内外学者进行了相关研究，但大多采用数值模拟的方法建立易损性曲线，而基于历史震害数据建立的易损性模型还比较少。WANG等[3]提出了一种新的损伤分类标准，以分类和量化隧道损伤收集的大地震数据。周志光等[4]采用时程分析的方法，利用ABAQUS建立了土与隧道的局部模型，计算了软土隧道的地震易损性。王伯超等[5]采用增量动力分析（incremental dynamic analysis，IDA）法计算了以峰值地面加速度（peak ground acceleration，PGA）、峰值地面位移（peak ground displacement，PGD）、谱加速度（spectral acceleration，Sa）为地震强度参数下的公路隧道地震易损性，结果发现采用PGA作为地震强度参数时所得到的IDA计算结果离散性最小。董正方等[6]利用SAP2000，采用修正IDA法计算了不同PGA下的隧道地震易损性。苏琪等[7]引入双地震动强度参数，采用IDA法进行易损性分析，将得到的易损性曲面与经验易损性曲线进行对比。禹海涛等[8]考虑沉管隧道结构特征及接头构造，通过等效线性化方法来描述地层的非线性特征，给出了纵向地震易损性分析模型。黄忠凯等[9]考虑场地土层、地震波的不确定性以及土-结构接触效应的影响，以衬砌截面弯矩承载能力比为损伤指标计算得到了隧道地震易损性曲线。陈之毅等[10]采用概率密度演化法得到隧道结构地震作用下的变形响应概率分布，结合变形指标计算了随机地震作用下的隧道结构可靠度。赵晓勇等[11]结合实际工程中得到的损失比数据，对都汶公路4座隧道进行了震害损失快速评估。
目前，建立隧道地震易损性模型的方法可以分为2种，一种是基于实际震害数据回归得到的地震易损性模型，另一种是基于有限元计算数据回归得到的地震易损性模型。第一种方式基于历史震害数据，结合易损性模型，回归得到的易损性曲线称为经验易损性曲线，具有很高的可靠性和实用价值。第二种方式通过建立隧道有限元模型，输入选取好的一系列地震动记录，对隧道响应进行回归分析，获得隧道地震易损性曲线，对于隧道震害资料匮乏的地区是一种很好的解决办法。汶川地震有着大量的隧道震害数据，这为建立隧道的经验地震易损性曲线提供了数据基础。
在地震频发的山区，隧道被视为生命线的重要组成部分，隧道一旦发生破坏将严重拖慢抢险救灾的进度，因此，对山区隧道的易损性研究十分必要。易损性函数描述了在特定的地震强度下结构受损的可能性，因此本文选择易损性曲线的形式，以汶川地震收集的实际震害资料为基础，通过极大似然估计的方式，回归分析得到山区隧道的地震易损性模型。另外，结合地震损失比的概念，发展了隧道地震平均损失率模型，可以更快速地评估隧道结构在未来地震中的损失，并为地震保险提供参考。
1　震害调查
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通过对四川、甘肃、陕西地震灾区内国省干道以及部分县乡道路的广泛调研，对六至十一烈度区，共计18条线路56座隧道进行了震害统计。研究发现，隧道可以分为洞口浅埋段、洞口过渡段、普通段以及断层破碎段。在汶川地震中，跨越断层的断层破碎段隧道结构破坏最为严重，而洞口由于是隧道唯一暴露在外的结构部分，由于次生灾害的原因（落石，滑坡等），破坏也较为严重，相对地，普通段隧道结构震害最轻，一些典型的隧道震害如图1所示。
根据陈乐生[12]编写的《汶川地震公路震害调查》中所给出的隧道震害等级评价体系，隧道震害可以分为5个等级，即情况正常、结构轻微破坏、结构破坏、结构较严重破坏与结构严重破坏。通常来说，建筑结构在进行地震易损性分析时也将破坏等级分为5个等级，即基本完好、轻微破坏、中等破坏、严重破坏和毁坏。在本文中，为了便于隧道的震后快速评估，将隧道结构的破坏等级划分为5级，具体情况如表1所示。
本文整理了《汶川地震公路震害调查》[12]中提供的隧道震害资料，共计56座隧道。隧道的各类破坏等级占比如图2所示。其中绝大部分处于完好和轻微破坏状态，约占总体的79%左右，中等破坏占15%，而严重破坏和毁坏的比例则比较低，合计占总体的6%。
本文收集了隧道各部分的震害数据，按照洞口浅埋段、洞口过渡段、普通段、断层破碎段以及隧道整体进行了震害统计与回归分析，最终得到了隧道各组成部分的易损性模型。
2　地震动参数确定
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地震动强度参数（intensity measure，IM）的选取对结构易损性分析与模型的建立至关重要，在以往的结构地震易损性研究中，有不少学者选择谱加速度（Sa）作为地震动强度参数（IM）[13-15]，然而以谱加速度作为地震动强度参数（IM）首先需要了解结构的基频，而对隧道结构来讲，以实际震害数据回归得到易损性模型面临着无法大量获得样本基频这一问题，因此本文选择更好获取的地震动峰值加速度（PGA）作为地震动参数。
本文采用LU等[16]回归分析得到的汶川地震动衰减模型，如式（1）所示：
式中：c1、c2为衰减系数，取值见表2；R为隧道距断层破裂面的最短距离（km）；h为震源深度影响系数，取25。
地震动衰减关系模型表达式中不仅包含了与距离及震源相关的系数，还包含了标准差，其反映了地震动固有的离散性，由表2可知，3个分量的标准差δ从0.286变化至0.303。
对于震级较大的情况会有断层出现，这时不能采用点源模型而需要采用线源模型计算断层距[17]。因此，本文采用CAMPBELL[18]提出的断层距计算模型，对于隧道结构的经纬度获取可以采用百度坐标拾取系统来得到[18]，最后按照式（1）计算样本隧道位置的PGA。
3　隧道易损性模型的建立
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3.1　地震易损性分析方法
易损性函数的选择要合理，要能够较好地体现地震动强度（IM）与结构破坏之间的关系，本文以双参数对数正态分布函数作为易损性函数[19]，表达式为
式中：F（a）为结构的易损性函数；a为地震动强度（IM），本文选取PGA作为IM；Ф[ ]为标准正态分布函数；c与ζ分别为中位值与对数标准差。
极大似然估计（maximum likehood estimate，MLE）有着对任何总体都适用的优点，为了能够求出中位值c与对数标准差ζ，本文采用独立估计的极大似然估计方法[20]，似然函数的表达式为
式中：F（ ）为结构某一损伤等级下的易损性函数，本文中表现形式如式（2）所示；N为隧道的总数；ai为第i座隧道的峰值地面加速度（PGA）；xi为伯努利随机事件取值，当PGA = ai时，隧道达到对应破坏等级，xi = 1，反之xi = 0。
依据前文给出的方法得到隧道处的PGA便可以建立起“隧道序号-破坏状态-隧道处PGA”样本，表3与表4分别为隧道整体样本震害矩阵与隧道洞口浅埋段样本震害矩阵示例，其中0代表该破坏等级未发生，1代表该破坏等级发生，根据统计得到的震害矩阵通过极大似然估计便可求解出地震易损性函数中的c与ζ。在填写样本数据时遵循以下2个原则：①分段隧道统计样本数据填写过程中，最重破坏等级及以下的破坏等级栏目中均填“1”；②整体隧道样本统计中，按照该隧道的各分段隧道破坏样本中最重破坏等级的样本填写破坏情况。
3.2　隧道结构地震易损性
采用来自汶川地震的56座隧道震害数据，通过极大似然估计分别得到了隧道整体、洞口浅埋段、洞口过渡段、普通段和断层破碎带段的地震易损性曲线，图3为隧道整体地震易损性曲线，易损性模型的回归参数如表5所示。可以发现伴随地震动强度（PGA）的增加，各等级破坏状态的超越概率都在不断增长。轻微破坏状态下的地震易损性曲线在0.4 g之前增长明显，严重破坏及毁坏状态的地震易损性曲线在0.6 g之前增长缓慢。
隧道结构整体及各部分的地震易损性曲线，如图4（a）~（d）所示。隧道各部分的地震易损性模型参数，如表6~表9所示。可以看出，在轻微破坏条件下，洞口浅埋段的易损性要高于洞口过渡段、普通段和断层破碎带段，这是因为洞口过渡段岩体一般为强风化底层，其力学指标普遍低于下覆岩体，且洞口极易发生边坡崩塌及落石，这些因素都会对洞口浅埋段地震易损性造成负面影响。
随着破坏程度的增加，断层破碎带段的地震易损性逐渐高于隧道其他部分，这是因为在地震作用下断层破碎带上下盘地震动位移及应力差异大，破坏相对严重，而隧道其他部分处于周围岩体的强约束之中，在地震作用下一起运动，破坏相对较轻，由于调查的56座隧道只有断层破碎段发生毁坏，其他部分都未发生毁坏，因此毁坏条件下隧道整体易损性与隧道断层破碎段易损性相同。
4　隧道地震平均损失率模型
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损失比是指结构发生某一程度破坏时，用来修复的费用与重建结构所需费用的比值。概率损失模型表达形式为结构不同破坏状态的损失比与概率易损性曲线中不同破坏状态发生概率的乘积之和，如式（4）所示：
式中：RM为平均损失率；Pi为i等级破坏的发生概率；Ri为i等级破坏的损失比，i = 1~5，数字含义分别为完好、轻微破坏、中等破坏、严重破坏以及毁坏。
国家标准GB/T 18208.4—2011《地震现场工作第4部分：灾害直接损失评估》[21]给出的公路系统工程结构的破坏损失比，如表10所示。
在进行平均损失率计算时，基本完好损失比取0，毁坏损失比取100，其余破坏状态损失比取表10中位值，由式（4）及表10结合汶川隧道地震易损性模型就可以求出隧道的地震平均损失率，如图5所示。随着PGA的增加，隧道平均损失率逐渐增长，且增长趋势近似线性。
在地震发生后可以根据此模型快速地估算出隧道结构破坏造成的经济损失。同时，该模型可以为地震保险等行业提供技术参考。
5　结论
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本文基于汶川地震震害资料，选择地震动峰值加速度（PGA）作为地震动参数，以双参数对数正态分布作为易损性函数，利用极大似然估计得到的隧道结构整体及各部分的地震易损性曲线，得到的主要结论如下：
1）本文根据汶川隧道震害资料，通过回归的方式得到了山区隧道整体地震易损性模型，轻微破坏状态下的地震易损性曲线在0.4 g之前增长明显，毁坏状态下的地震易损性曲线在0.6 g之前增长缓慢。
2）轻微破坏条件下，洞口浅埋段的地震易损性高于洞口过渡段、普通段和断层破碎带段，这是因为洞口段岩体一般为强风化地层，其力学指标普遍低于下覆岩体，且洞口极易发生洞口边坡崩塌及落石，这些因素都会对洞口浅埋段地震易损性造成负面影响。
3）随着破坏程度的增加，断层破碎带段的地震易损性逐渐高于隧道其他部分，这是因为在地震作用下断层破碎带上下盘地震动位移及应力差异大，破坏相对严重，而隧道其他部分处于周围岩体的强约束之中，在地震作用下一起运动，破坏相对较轻。
4）结合隧道结构发生某一种破坏状态时的损失比，建立了隧道的平均损失率模型，依据本文建立的隧道易损性模型及隧道平均损失率模型可以在将来发生类似地震时快速地进行地震损失评估。
基金
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  • 国家自然科学基金地震科学联合基金重点项目(U2239252)
  • 湖州职业技术学院高层次人才专项课题(2022GY22)
  • 湖州职业技术学院校级规划课题(2022ZD03)
文献
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2024年第44卷第3期
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doi: 10.13197/j.eeed.2024.0318
  • 接收时间：2024-01-26
  • 首发时间：2026-03-30
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  • 收稿日期：2024-01-26
  • 修回日期：2024-03-16
基金
国家自然科学基金地震科学联合基金重点项目(U2239252)
湖州职业技术学院高层次人才专项课题(2022GY22)
湖州职业技术学院校级规划课题(2022ZD03)
作者信息
    1.湖州职业技术学院 建筑工程学院，浙江 湖州 313000
    2.湖州市绿色建筑技术重点实验室，浙江 湖州 313000
    3.东北石油大学 土木建筑工程学院，黑龙江 大庆 163318
    4.黑龙江省寒区新能源热利用及防灾减灾重点实验室，黑龙江 大庆 163318
    5.黑龙江省教育厅防灾减灾及防护工程重点实验室，黑龙江 大庆 163318
    6.核工业湖州勘测规划设计研究院股份有限公司，浙江 湖州 313000

通讯作者:

李廷辉（1992—），男，讲师，博士，主要从事生命线工程抗震及易损性研究。E-mail：
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2种不同金属材料的力学参数
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species		 占总种数比例
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total species (%)		 属
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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
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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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