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Article(id=1227614517392240801, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227614514896634485, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.04.003, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1655049600000, receivedDateStr=2022-06-13, revisedDate=1664208000000, revisedDateStr=2022-09-27, acceptedDate=null, acceptedDateStr=null, onlineDate=1770615708920, onlineDateStr=2026-02-09, pubDate=1714233600000, pubDateStr=2024-04-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770615708920, onlineIssueDateStr=2026-02-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770615708920, creator=13701087609, updateTime=1770615708920, updator=13701087609, issue=Issue{id=1227614514896634485, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='4', pageStart='539', pageEnd='728', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770615708325, creator=13701087609, updateTime=1770795248114, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228367559410512191, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227614514896634485, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228367559410512192, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227614514896634485, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=556, endPage=564, ext={EN=ArticleExt(id=1227614517740368035, articleId=1227614517392240801, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Influence of groundwater level on the seismic response of nuclear power structure, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Most of the nuclear power plants are built around the coastal or along the rivers. Below the underground water level，distribution of the water in the soil pore has a great influence on the seismic response of soil，which affects the response of the nuclear power plants. To analyze the effect of the underground water level on the seismic response of nuclear power plant，a saturated porous medium model considering the interaction of the saturated soil and structure is used in this paper. Firstly，the free field of the horizontal layered site of dry soil-saturated soil is obtained by the transfer matrix method，and the wave input of soil-structure interaction analysis is realized combined with the transmission boundary； Then，the partitioned parallel calculation method of soil-structure interaction is used to analyze the saturated soil-structure interaction. The soil with groundwater level is described by the generalized saturated porous medium model which is simulated by the lumped-mass explicit finite element combined with the transmission boundary using the self-programmed FORTRAN code，and the structure is analyzed by ANSYS using implicit finite element. Taking a nuclear power plant as an example，the dynamic response of soil-base-nuclear power plant system is analyzed in five sites with different groundwater levels of -10 m，-20 m，-30 m and -40 m，as well as pure saturated soil. The results show that the groundwater level has a great influence on the response of foundation and structure. For the calculation example in this paper，the results show that the groundwater level has little effect on the displacement of the foundation and structure，but has a great effect on the acceleration of the foundation and structure.

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核电结构大多沿海或沿江、河而建，在地下水位以下，土体孔隙中的流体对土层的地震响应有较大影响，进而影响核电结构的响应。本文采用饱和多孔介质模型，考虑土-结相互作用效应，分析地下水位对核电结构地震反应的影响。通过传递矩阵方法，得到干土-饱和土水平成层场地的自由场，并结合透射人工边界，实现土-结相互作用分析的波动输入；采用土-结相互作用的分区并行计算方法，实现饱和土和结构相互作用分析。其中，含地下水位的场地土体采用广义饱和多孔介质模型描述，通过自编FORTRAN程序用集中质量显式有限元结合透射人工边界进行模拟，结构通过ANSYS中的隐式有限元进行分析。以某一核电结构为例，分析了0，-10，-20，-30，-40 m不同地下水位的五种场地上，土-基础-核电结构体系的动力响应。结果表明，地下水位对基础和结构的位移影响不大，对加速度的影响较大。

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陈少林（1974—），男，博士，教授。E-mail： 。
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吴绍恒（1996—），男，硕士研究生。E-mail： 。

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吴绍恒（1996—），男，硕士研究生。E-mail： 。

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吴绍恒（1996—），男，硕士研究生。E-mail： 。

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Earthquake Engineering and Engineering Vibration， 2010， 30（2）： 24-31., articleTitle=A direct time-domain method for analysis of three-dimensional soil-structure dynamic interaction, refAbstract=null), Reference(id=1227639808890171705, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, doi=null, pmid=null, pmcid=null, year=2017, volume=47, issue=12, pageStart=1321, pageEnd=1330, url=null, language=null, rfNumber=［31］, rfOrder=44, authorNames=陈少林, 王俊泉, 刘启方, journalName=中国科学：技术科学, refType=null, unstructuredReference=陈少林， 王俊泉， 刘启方， 等. 基于显-隐式格式的三维时域土-结相互作用分析的异步并行算法［J］. 中国科学：技术科学， 2017， 47（12）： 1321-1330., articleTitle=基于显-隐式格式的三维时域土-结相互作用分析的异步并行算法, refAbstract=null), Reference(id=1227639808978252093, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, doi=null, pmid=null, pmcid=null, year=2017, volume=47, issue=12, pageStart=1321, pageEnd=1330, url=null, language=null, rfNumber=［31］, rfOrder=45, authorNames=Chen Shaolin, Wang Junquan, Liu Qifang, journalName=Scientia Sinica Technologica, refType=null, unstructuredReference=Chen Shaolin， Wang Junquan， Liu Qifang， et al. 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A method for three-dimensional saturated soil-foundation-structure dynamic interaction analysis［J］. Chinese Journal of Theoretical and Applied Mechanics， 2016， 48（6）： 1362-1371., articleTitle=A method for three-dimensional saturated soil-foundation-structure dynamic interaction analysis, refAbstract=null), Reference(id=1227639809280241995, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, doi=null, pmid=null, pmcid=null, year=1984, volume=3, issue=4, pageStart=174, pageEnd=183, url=null, language=null, rfNumber=［33］, rfOrder=48, authorNames=Liao Z P, Wong H L, journalName=International Journal of Soil Dynamics and Earthquake Engineering, refType=null, unstructuredReference=Liao Z P， Wong H L. A transmitting boundary for the numerical simulation of elastic wave propagation［J］. International Journal of Soil Dynamics and Earthquake Engineering， 1984， 3（4）： 174-183., articleTitle=A transmitting boundary for the numerical simulation of elastic wave propagation, refAbstract=null)], funds=[Fund(id=1227639803487907973, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, awardId=U2039209, language=CN, fundingSource=国家自然科学基金资助项目(U2039209), fundOrder=null, country=null), Fund(id=1227639803605348490, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, awardId=51978337, language=CN, fundingSource=国家自然科学基金资助项目(51978337), fundOrder=null, country=null), Fund(id=1227639803685040270, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, awardId=null, language=CN, fundingSource=华龙一号及在役核电机组关键技术装备攻关工程项目——核电厂结构分析软件资助项目, fundOrder=null, country=null)], companyList=[AuthorCompany(id=1227639796152071038, tenantId=1146029695717560320, journalId=1225147924628267009, 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tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, language=EN, label=Tab.1, caption=

Material parameters of nuclear power plants

, figureFileSmall=null, figureFileBig=null, tableContent=
结构组成部分弹性模量/(1010 N·m-2)泊松比密度/（kg·m-3）
水箱3.170.172450
锥形屋顶3.190.172369
外部冷却空气入口3.270.172180
混凝土安全壳3.290.172168
辅助厂房2.490.172400
钢制安全壳21.00.307750
), ArticleFig(id=1227639802766487650, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, language=CN, label=表1, caption=

核电结构的材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
结构组成部分弹性模量/(1010 N·m-2)泊松比密度/（kg·m-3）
水箱3.170.172450
锥形屋顶3.190.172369
外部冷却空气入口3.270.172180
混凝土安全壳3.290.172168
辅助厂房2.490.172400
钢制安全壳21.00.307750
), ArticleFig(id=1227639802846179429, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, language=EN, label=Tab.2, caption=

Parameters of dry soil

, figureFileSmall=null, figureFileBig=null, tableContent=
参数土层
Dry 1Dry 2Dry 3
厚度/m202020
密度/(kg·m-3)176220832403
剪切模量/(109 N·m-2)0.330.771.42
泊松比0.350.300.25
阻尼系数0.020.020.02
剪切波速/(m·s-1)433608769
压缩波速/(m·s-1)90111371332
), ArticleFig(id=1227639802963619946, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, language=CN, label=表2, caption=

干土土体参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数土层
Dry 1Dry 2Dry 3
厚度/m202020
密度/(kg·m-3)176220832403
剪切模量/(109 N·m-2)0.330.771.42
泊松比0.350.300.25
阻尼系数0.020.020.02
剪切波速/(m·s-1)433608769
压缩波速/(m·s-1)90111371332
), ArticleFig(id=1227639803081060464, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, language=EN, label=Tab.3, caption=

Parameters of saturated soil

, figureFileSmall=null, figureFileBig=null, tableContent=
参数土层
Sat1Sat2Sat3
厚度h/m202020
固相密度/(kg·m-3)176220832403
液相密度/(kg·m-3)100010001000
孔隙率0.300.350.40
固体体积模量Ks/(1010 N·m-2)2.833.253.70
液体体积模量Kf/(109 N·m-2)2.182.182.18
骨架体积模量Kfr/(109 N·m-2)4.306.207.80
骨架剪切模量Gfr/(109 N·m-2)0.330.771.42
流体动力黏度0.0010.0010.001
渗透率/(10-7)6.005.004.00
泊松比υ0.350.300.25
阻尼系数ζ0.020.020.02
剪切波速Vs/(m·s-1)517754992
快波压缩波速Vp/(m·s-1)247025722733
), ArticleFig(id=1227639803160752246, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, language=CN, label=表3, caption=

饱和土土体参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数土层
Sat1Sat2Sat3
厚度h/m202020
固相密度/(kg·m-3)176220832403
液相密度/(kg·m-3)100010001000
孔隙率0.300.350.40
固体体积模量Ks/(1010 N·m-2)2.833.253.70
液体体积模量Kf/(109 N·m-2)2.182.182.18
骨架体积模量Kfr/(109 N·m-2)4.306.207.80
骨架剪切模量Gfr/(109 N·m-2)0.330.771.42
流体动力黏度0.0010.0010.001
渗透率/(10-7)6.005.004.00
泊松比υ0.350.300.25
阻尼系数ζ0.020.020.02
剪切波速Vs/(m·s-1)517754992
快波压缩波速Vp/(m·s-1)247025722733
), ArticleFig(id=1227639803236249719, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, language=EN, label=Tab.4, caption=

Parameter combination of dry soil and saturated soil under different groundwater levels

, figureFileSmall=null, figureFileBig=null, tableContent=
算例地下水位GL/m土层厚度组合/m土体类型组合
1020+20+20Sat1+Sat2+Sat3
2-1010+10+20+20Dry1+Sat1+Sat2+Sat3
3-2020+20+20Dry1+Sat2+Sat3
4-3020+10+10+20Dry1+Dry2+Sat2+Sat3
5-4020+20+20Dry1+Dry2+Sat3
), ArticleFig(id=1227639803315941500, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517392240801, language=CN, label=表4, caption=

不同地下水位下干土和饱和土参数组合

, figureFileSmall=null, figureFileBig=null, tableContent=
算例地下水位GL/m土层厚度组合/m土体类型组合
1020+20+20Sat1+Sat2+Sat3
2-1010+10+20+20Dry1+Sat1+Sat2+Sat3
3-2020+20+20Dry1+Sat2+Sat3
4-3020+10+10+20Dry1+Dry2+Sat2+Sat3
5-4020+20+20Dry1+Dry2+Sat3
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地下水位对核电结构地震反应的影响分析
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吴绍恒 1 , 陈少林 1 , 刘鸿泉 1 , 孙晓颖 2, 3
振动工程学报 | 2024,37(4): 556-564
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振动工程学报 | 2024, 37(4): 556-564
地下水位对核电结构地震反应的影响分析
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吴绍恒1 , 陈少林1 , 刘鸿泉1, 孙晓颖2, 3
作者信息
  • 1南京航空航天大学土木与机场工程系，江苏　南京　210016
  • 2中国地震局工程力学研究所，黑龙江　哈尔滨　150080
  • 3中国核电工程有限公司，北京　100840

    • 吴绍恒（1996—），男，硕士研究生。E-mail： 。

通讯作者:

陈少林（1974—），男，博士，教授。E-mail： 。
Influence of groundwater level on the seismic response of nuclear power structure
Shao-heng WU1 , Shao-lin CHEN1 , Hong-quan LIU1, Xiao-ying SUN2, 3
Affiliations
  • 1Department of Civil and Airport Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
  • 2Institute of Engineering Mechanics, CEA, Harbin 150080, China
  • 3China Nuclear Power Engineering Co., Ltd., Beijing 100840, China
出版时间: 2024-04-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.04.003
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摘要
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核电结构大多沿海或沿江、河而建，在地下水位以下，土体孔隙中的流体对土层的地震响应有较大影响，进而影响核电结构的响应。本文采用饱和多孔介质模型，考虑土-结相互作用效应，分析地下水位对核电结构地震反应的影响。通过传递矩阵方法，得到干土-饱和土水平成层场地的自由场，并结合透射人工边界，实现土-结相互作用分析的波动输入；采用土-结相互作用的分区并行计算方法，实现饱和土和结构相互作用分析。其中，含地下水位的场地土体采用广义饱和多孔介质模型描述，通过自编FORTRAN程序用集中质量显式有限元结合透射人工边界进行模拟，结构通过ANSYS中的隐式有限元进行分析。以某一核电结构为例，分析了0，-10，-20，-30，-40 m不同地下水位的五种场地上，土-基础-核电结构体系的动力响应。结果表明，地下水位对基础和结构的位移影响不大，对加速度的影响较大。

土-结相互作用  /  核电结构  /  地下水位  /  饱和多孔介质  /  集中质量显式有限元  /  人工边界

Most of the nuclear power plants are built around the coastal or along the rivers. Below the underground water level，distribution of the water in the soil pore has a great influence on the seismic response of soil，which affects the response of the nuclear power plants. To analyze the effect of the underground water level on the seismic response of nuclear power plant，a saturated porous medium model considering the interaction of the saturated soil and structure is used in this paper. Firstly，the free field of the horizontal layered site of dry soil-saturated soil is obtained by the transfer matrix method，and the wave input of soil-structure interaction analysis is realized combined with the transmission boundary； Then，the partitioned parallel calculation method of soil-structure interaction is used to analyze the saturated soil-structure interaction. The soil with groundwater level is described by the generalized saturated porous medium model which is simulated by the lumped-mass explicit finite element combined with the transmission boundary using the self-programmed FORTRAN code，and the structure is analyzed by ANSYS using implicit finite element. Taking a nuclear power plant as an example，the dynamic response of soil-base-nuclear power plant system is analyzed in five sites with different groundwater levels of -10 m，-20 m，-30 m and -40 m，as well as pure saturated soil. The results show that the groundwater level has a great influence on the response of foundation and structure. For the calculation example in this paper，the results show that the groundwater level has little effect on the displacement of the foundation and structure，but has a great effect on the acceleration of the foundation and structure.

soil-structure interaction  /  nuclear power structure  /  groundwater level  /  saturated porous media  /  lumped-mass explicit finite element  /  artificial boundary
吴绍恒, 陈少林, 刘鸿泉, 孙晓颖. 地下水位对核电结构地震反应的影响分析. 振动工程学报, 2024 , 37 (4) : 556 -564 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.04.003
Shao-heng WU, Shao-lin CHEN, Hong-quan LIU, Xiao-ying SUN. Influence of groundwater level on the seismic response of nuclear power structure[J]. Journal of Vibration Engineering, 2024 , 37 (4) : 556 -564 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.04.003
正文
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引言
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核电已经成为重要的清洁能源。核电项目的选址和勘探已经在沿海地区进行，并延伸到内陆沿江地区。在这些地区，地下水位通常较浅，地基中部分土体是饱和土。一些震害数据表明，当地基土为饱和土时，其震害与干土有显著差异，地下水位变化也会对地震反应产生重大影响。
对场地地震反应的研究表明，地下水位的变化对地表加速度峰值、位移峰值等的放大作用有一定的影响［1-3］。路堤、边坡、水坝等构筑物在地震作用下，由于地下水位的变化，对其地震响应及稳定性也会产生不利影响［4-6］。以往对核电结构土-结相互作用的研究主要集中在干土情形［7-10］，而对考虑饱和土的土-结相互作用的相关研究还是比较少的。实际工程中，常常以地下水位为分界线，水位以上是干土，以下是饱和土。地下水位对核电地震反应的影响如何，目前仍缺乏相关认识。目前中国核电抗震设计规范对地下水位影响问题没有明确的规定和要求。在美国规范ASCE/SEI4-16［11］中有提到“在一些分析中，地下水的影响是通过增加地下水位以下土体的泊松比来考虑的，但用来表示地下水影响的泊松比应该得到验证”“对于较浅的饱和土体（即地下水位以下的土体），纵波速度通常受水的控制，约为1500 m/s”。以上规范里的内容提供了一种通过改变土体的纵波波速，调整干土泊松比来近似考虑地下水影响的方法。这种方法无需考虑饱和土力学模型，比较简便，但其适用性有待验证。
饱和土-结系统在地震波作用下的响应分析可看作是地震波在饱和介质中的散射问题。一般先讨论饱和介质中的地震波传播问题，即入射场（或自由场）分析。Biot等［12-14］建立了弹性波在饱和多孔介质中的传播理论，为研究饱和介质中波的传播奠定了基础。Deresiewicz等［15-18］在Biot理论的基础上，系统地研究了波在饱和土界面的传播特性，并且使用传递矩阵法分析了垂直入射时平面波在层状多孔介质中的反射与透射。此后，Jocker等［19］通过对Thomson-Haskell传递矩阵法的推广，得到了一种封闭形式的解析式，由此计算水平成层多孔介质的反射系数、透射系数，并验证了这种传递矩阵法的稳定性范围，提出了一些影响稳定性的因素。Yang［20］研究了SV波入射时，饱和土和其下方基岩组成的体系的自由场地的响应。赵宇昕等［21］通过传递矩阵法研究了水平成层饱和场地的自由场响应，该方法可以考虑地下水位的影响。
只有较为简单的土-结相互作用才有解析解［22-24］，一般情形需要借助数值方法，如通过有限元和人工边界条件进行求解。Liang等［25］和Han等［26］将土-结相互作用的研究由单相弹性土拓展到饱和土领域，采用间接边界元法分析了二维线性饱和土-结相互作用问题，分析了P-SV波斜入射时，土层深度、孔隙率、土层与基岩间的刚度比等参数的影响。Song等［27］采用直接有限元法分析饱和土与结构之间的非线性动力相互作用。但对于真实厂址地质，需要考虑干土上覆饱和土情形。若分别采用饱和土和干土模型，并考虑其界面连续条件，不同介质之间的耦合较为复杂。实际上，干土可看作孔隙率为零的饱和土的特殊情形，可通过广义饱和多孔介质模型进行描述，这样可将地下水位情形的场地分析统一用广义饱和多孔介质模型进行描述，将问题简化。
本文首先采用广义饱和多孔介质模型，将干土和饱和土统一到广义饱和多孔介质分析框架［28-29］，进而可分析考虑地下水位情形的场地反应。然后，采用土-结构动力相互作用分析的分区并行方法［30-32］，实现三维广义饱和土-基础-结构动力相互作用分析，并通过算例，分析不同地下水位对核电结构地震反应的影响。
1　基本理论
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1.1　土体内结点运动
根据Biot理论，可以将饱和弹性多孔介质的动力方程表示为：
式中　 u为固相位移；U为液相位移；D，N，Q，R为四个常数；，，，，，为固体骨架密度，为流体密度，为固、液两相惯性耦合质量密度；为一衰减函数，为流体动力黏度，为孔隙率，为渗透率。
利用伽辽金方法对式（1）和（2）进行有限元离散，并且在考虑边界条件的基础上，建立任意一个结点i的固、液相的有限元空间离散方程。考虑任一内结点i及其相邻结点构成的结点系，设结点i对应此结点系中某一单元的结点编号k，即存在某一对应关系k=k（i），则结点i的解耦的运动平衡方程为：
式中　 N为结点i对应的结点系中包含的单元总数；J为单元e的总结点数；为集中在i结点上的固相质量；为集中在i结点上的液相质量；，，，为单元刚度矩阵；，，，为单元阻尼矩阵，主要是由于固相和液相之间的相对运动所产生；在任意一个单元e中，需要对节点i分配载荷，其中为固相载荷矢量，为液相载荷矢量。
在研究饱和土体内部结点运动的过程中，我们还可以对固相部分添加瑞利阻尼用以描述骨架黏滞阻尼：
那么，式（3）可修正为：
通过中心差分与单边结合的积分格式，对内节点方程（6）和（4）进行时域积分：
式中　上标p为时刻；W=u，U，为位移矢量；Δt为时间离散步长；为p时刻的加速度；为p时刻速度。将式（7）代入式（4）和（6）可得到节点i的固相位移和液相位移公式为：
1.2　人工边界点运动
由于选取了有限的土体场地，为了模拟外行波穿过人工边界，我们采用多次透射公式［33］：
式中　 N为透射的阶数；为人工边界节点o在时刻的散射场位移；表示边界点o内部沿法线方向第n个透射点在时刻的散射场位移。
已知总场位移和自由场位移，可以通过两者相减得到散射场位移，即：
式中　 可以由上节所述的集中质量显示有限元方法求得。
通过透射公式求得边界节点的散射场位移后，便能通过以下公式求得边界点的总场位移。
式（10）~（13）可用于固、液相位移。对于水平成层饱和场地的自由场计算，具体可见文献［21］。
1.3　基础的运动
基础主要是通过传递作用力连接土体和上部结构，并且基础会在两者的合力作用下运动。
式中　 MF表示基础的集中质量矩阵；FS为结构对基础的作用力；FD为土体对基础的作用力，具体见文献［32］。
在得到每一时刻的作用力FD与FS后，运用中心差分法可得：
最后，由于假定基础是刚性的，可采用下式得到与基础接触的饱和土的土体点和核电结构的结构点的位移：
式中　矩阵A表示接触点和基础质心两者之间的坐标转换关系。
1.4　上部结构的运动
对于上部核电结构，使用ANSYS进行计算，其动力学方程可写成：
可采用Newmark时步积分方法进行求解。
上面介绍了广义饱和土统一框架下，土-结相互作用的分区计算方法和流程，其中将干土和饱和土统一到广义饱和多孔介质分析框架的可行性验证见文献［28-29］，土-结动力相互作用分析的分区并行方法验证见文献［31-32］。
2　计算模型及工况
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2.1　结构模型
核电厂（CAP1400）的核岛分为两部分，即反应堆厂房和辅助厂房。反应堆厂房分为三个部分，即水箱、钢筋混凝土安全壳（或屏蔽厂房）、钢制安全壳和内部结构，如图1所示。
结构总高度约为91.250 m，最大平面尺寸为56.120 m×90.800 m。锥形屋顶与水箱相连。辅助厂房三面环绕屏蔽厂房布置，高度分别为34.700，37.200，51.200 m。利用有限元软件ANSYS建立了CAP1400核电厂的有限元模型，结构单元总数为35162，对应的节点总数为32467。采用刚性基础，尺寸为 92 m×60 m×16 m。由于模型的复杂性，在模型与实际核电厂相似的基础上，对模型进行了简化。模型的建立采用了几种典型的元素类型，如SHELL181，SOILD185和MASS21。材料参数列于表1。
2.2　场地模型
所研究的三维场地体系是由三层土体组成，第三层土体以下为半空间的无限域，参数与第三层相同。土体计算区域的尺寸为640 m×360 m×60 m，土体离散为2 m×2 m×2 m的六面体八节点实体单元。单元总数和节点总数分别为1738560和1835579。表2列出了干土土体的参数。表3列出了饱和土土体的参数，表中的渗透率与渗透系数满足，其中，为渗透系数。经过校验，本文中的土体模型满足波动的精度要求（，其中，为单元尺寸；为最小波长）。
2.3　工况
由于要考虑不同地下水位的情形，所以将上面的干土和饱和土参数，根据地下水位的不同进行组合，具体工况组合如表4所示。
3　模拟结果及分析
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为了使核电结构土-结相互作用的数值模拟更加准确，选取真实地震动时程作为输入，对核电结构土-结相互作用进行分析。本文以美国核管会导则RG1.60规定的水平方向标准地震反应谱为设计地震反应谱，依据该反应谱在PEER数据库中选取了三条水平向的强震记录进行数值模拟，激励方向沿模型x坐标轴方向。其中三条水平向地震记录（RSN740_LOMAP_ADL250（地震波1），RSN1083_NORTHR_GLE170（地震波2），RSN3750_CAPEMEND_LFS270（地震波3））在调幅后的位移时程、加速度时程以及加速度傅里叶谱如图2所示。
图3和4分别为地震波1在不同地下水位下地表位移和加速度的时程曲线以及三条地震波的峰值放大系数随地下水位的变化曲线。从图3可以看出，地下水位的变化对地震波作用下地表的位移响应影响不大。从图4可以看出，地下水位对地表的加速度响应有明显影响。随着地下水位的上升，地表峰值加速度的放大系数先减小后增大。
图5和6分别为地震波1在不同地下水位下基础位移和加速度的时程曲线以及三条地震波的峰值放大系数变化曲线。同样，地下水位对基础的位移响应影响不大，对加速度有明显影响，加速度峰值放大系数随着地下水位升高而增大。
图7和8分别为地震波1在不同地下水位下核电结构顶部位移和加速度的时程曲线以及三条地震波的峰值放大系数变化曲线。由图可知，所呈现的规律总体上与上述的规律基本一样，但地下水位对结构顶部反应的影响要比对基础的影响更大。
图9给出了地震波1，2和3在不同地下水位条件下场地表面、基础以及核电结构顶部三个不同位置处的加速度反应谱以及三者的谱加速度峰值变化曲线。由加速度反应谱可以看出，地下水位对加速度反应谱的影响主要在2~10 Hz频段；总体而言，谱加速度峰值随着地下水位升高而增大。
4　结论
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本文实现了一种考虑地下水位情形的核电结构土-结相互作用分析分区计算方法，分析了地震波作用下地下水位变化对场地、基础和核电结构动力响应的影响。针对本文算例，得出以下结论：
（1） 在地震波作用下，地下水位的变化对场地、基础和核电结构的位移影响不明显，对加速度响应有显著影响。
（2） 随着地下水位上升，场地、基础和核电结构的加速度峰值逐渐增大，且结构加速度峰值比基础的增加更快，即地下水位对核电结构反应的影响比对基础和土体的更为明显。
（3） 地下水位对核电结构楼板加速度谱的影响较大，随着地下水位的升高，谱加速度峰值逐渐加大。
因此，在核电结构和设备抗震设计分析中，应合理地考虑地下水位的影响。另外，本文建立的考虑地下水位的土-结相互作用模型和分析方法可用于其他相关问题的分析，可进一步考虑土体液化引起的基础失效和结构破坏研究。
基金
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  • 国家自然科学基金资助项目(U2039209)
  • 国家自然科学基金资助项目(51978337)
  • 华龙一号及在役核电机组关键技术装备攻关工程项目——核电厂结构分析软件资助项目
文献
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［28］
陈少林， 柯小飞， 张洪翔. 海洋地震工程流固耦合问题统一计算框架［J］. 力学学报， 2019， 51（2）： 594-606.
Chen Shaolin， Ke Xiaofei， Zhang Hongxiang. A unified computational framework for fluid-solid coupling in marine earthquake engineering［J］. Chinese Journal of Theoretical and Applied Mechanics， 2019， 51（2）： 594-606.
［29］
陈少林， 程书林， 柯小飞. 海洋地震工程流固耦合问题统一计算框架——不规则界面情形［J］. 力学学报， 2019， 51（5）： 1517-1529.
Chen Shaolin， Cheng Shulin， Ke Xiaofei. A unified computational framework for fluid-solid coupling in marine earthquake engineering： irregular interface case［J］. Chinese Journal of Theoretical and Applied Mechanics， 2019， 51（5）： 1517-1529.
［30］
陈少林， 唐敢， 刘启方， 等. 三维土-结构动力相互作用的一种时域直接分析方法［J］. 地震工程与工程振动， 2010， 30（2）： 24-31.
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陈少林， 王俊泉， 刘启方， 等. 基于显-隐式格式的三维时域土-结相互作用分析的异步并行算法［J］. 中国科学：技术科学， 2017， 47（12）： 1321-1330.
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［32］
陈少林， 赵宇昕. 一种三维饱和土-基础-结构动力相互作用分析方法［J］. 力学学报， 2016， 48（6）： 1362-1371.
Chen Shaolin， Zhao Yuxin. A method for three-dimensional saturated soil-foundation-structure dynamic interaction analysis［J］. Chinese Journal of Theoretical and Applied Mechanics， 2016， 48（6）： 1362-1371.
［33］
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2024年第37卷第4期
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doi: 10.16385/j.cnki.issn.1004-4523.2024.04.003
  • 接收时间：2022-06-13
  • 首发时间：2026-02-09
  • 出版时间：2024-04-28
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  • 收稿日期：2022-06-13
  • 修回日期：2022-09-27
基金
国家自然科学基金资助项目(U2039209)
国家自然科学基金资助项目(51978337)
华龙一号及在役核电机组关键技术装备攻关工程项目——核电厂结构分析软件资助项目
作者信息
    1南京航空航天大学土木与机场工程系，江苏　南京　210016
    2中国地震局工程力学研究所，黑龙江　哈尔滨　150080
    3中国核电工程有限公司，北京　100840

通讯作者:

陈少林（1974—），男，博士，教授。E-mail： 。
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https://castjournals.cast.org.cn/joweb/zdgcxb/CN/10.16385/j.cnki.issn.1004-4523.2024.04.003
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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