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Article(id=1245389866096243586, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245389858412282468, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0219, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1670860800000, receivedDateStr=2022-12-13, revisedDate=1684252800000, revisedDateStr=2023-05-17, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853682301, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853682301, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853682301, creator=13701087609, updateTime=1774853682301, updator=13701087609, issue=Issue{id=1245389858412282468, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='2', pageStart='1', pageEnd='232', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774853680470, creator=13701087609, updateTime=1774854277127, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245392361031840387, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245389858412282468, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245392361031840388, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245389858412282468, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=183, endPage=193, ext={EN=ArticleExt(id=1245389866473730958, articleId=1245389866096243586, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Comparative analysis of seismic reference wave field selection methods based on viscoelastic artificial boundary, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Artificial boundaries are introduced to simulate the infinite domain in the analysis of soil-structure dynamic interaction, and the viscoelastic artificial boundary is one of the commonly used artificial boundaries. When the artificial boundary is used, the selection of the reference wave field as the input of seismic wave is very important, different reference wave field selection methods will lead to great differences in calculation accuracy. In this paper, four kinds of two-dimensional site models, including homogeneous half space, layered site, depressed terrain and underground structure are assumed. Then ANSYS finite element software and viscoelastic artificial boundary are used to simulate the above four site models considering SV wave vertical incidence and 30° oblique incidence. The calculation accuracy of three different reference wave fields is compared in detail. The results show that when the free wave field is selected as the reference wave field for all artificial boundaries of the soil-structure dynamic interaction calculation model, the accuracy of the calculation results is the highest.

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土-结构动力相互作用分析需要引入人工边界对无限域进行模拟，黏弹性人工边界是目前常用人工边界之一。在使用人工边界时，作为地震波动输入的地震波参考波场选取很关键，不同参考波场选取方法的计算精度有很大差异。假定均匀半空间、成层场地、凹陷地形和含地下结构等4种二维场地模型，采用ANSYS有限元软件结合黏弹性人工边界计算工具，考虑SV波垂直入射和30°倾斜入射2种情形，分别对采用3种不同参考波场输入的计算精度进行了详细比较，结果表明：当土-结构动力相互作用计算模型的所有人工边界均选用自由场作为参考波场时，计算结果精度最高。

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丁海平（1966—），男，教授，博士，主要从事地震工程和防灾减灾工程。E-mail：
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宋贞霞（1979—），男，讲师，博士，主要从事地震工程和防灾减灾工程。E-mail：

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宋贞霞（1979—），男，讲师，博士，主要从事地震工程和防灾减灾工程。E-mail：

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(in Chinese), articleTitle=Three-dimensional viscoelastic static-dynamic unified artificial boundary, refAbstract=null), Reference(id=1245389889248801701, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389866096243586, doi=null, pmid=null, pmcid=null, year=2015, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[24], rfOrder=41, authorNames=尹侯权, journalName=null, refType=null, unstructuredReference=尹侯权. 地震波斜入射时成层半空间场地反应分析方法及其应用[D]. 北京：北京工业大学，2015., articleTitle=地震波斜入射时成层半空间场地反应分析方法及其应用, refAbstract=null), Reference(id=1245389889320104870, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389866096243586, doi=null, pmid=null, pmcid=null, year=2015, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[24], rfOrder=42, authorNames=YIN Houquan, journalName=null, refType=null, unstructuredReference=YIN Houquan. A method for layered half-space site response under obliquely incident earthquake and its application[D]. Beijing: Beijing University of Technology, 2015. (in Chinese), articleTitle=A method for layered half-space site response under obliquely incident earthquake and its application, refAbstract=null), Reference(id=1245389889399796647, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389866096243586, doi=null, pmid=null, pmcid=null, year=2015, volume=9, issue=1, pageStart=173, pageEnd=194, url=null, language=null, rfNumber=[25], rfOrder=43, authorNames=ZHAO M, YIN H Q, DU X L, journalName=Earthquakes and Structures, refType=null, unstructuredReference=ZHAO M, YIN H Q, DU X L, et al. 1D finite element artificial boundary method for layered half space site response from obliquely incident earthquake[J]. Earthquakes and Structures, 2015, 9(1): 173-194., articleTitle=1D finite element artificial boundary method for layered half space site response from obliquely incident earthquake, refAbstract=null), Reference(id=1245389889504654248, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389866096243586, doi=null, pmid=null, pmcid=null, year=2017, volume=13, issue=null, pageStart=573, pageEnd=588, url=null, language=null, rfNumber=[26], rfOrder=44, authorNames=ZHAO M, GAO Z D, WANG L T, journalName=Earthquakes and Structures, refType=null, unstructuredReference=ZHAO M, GAO Z D, WANG L T, et al. Obliquely incident earthquake for soil-structure interaction in layered half space[J]. Earthquakes and Structures, 2017, 13: 573-588., articleTitle=Obliquely incident earthquake for soil-structure interaction in layered half space, refAbstract=null), Reference(id=1245389889592734635, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389866096243586, doi=null, pmid=null, pmcid=null, year=2021, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[27], rfOrder=45, authorNames=马笙杰, journalName=null, refType=null, unstructuredReference=马笙杰. 凸起地形与上覆土层对强地震动特性的影响研究[D]. 北京：中国地震局地球物理研究所，2021., articleTitle=凸起地形与上覆土层对强地震动特性的影响研究, refAbstract=null), Reference(id=1245389889693397933, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389866096243586, doi=null, pmid=null, pmcid=null, year=2021, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[27], rfOrder=46, authorNames=MA Shengjie, journalName=null, refType=null, unstructuredReference=MA Shengjie. Research on the influence of convex topography and overlying soil on the characteristics of strong ground motion[D]. Beijing: Institute of Geophysics China Earthquake Administration, 2021. (in Chinese), articleTitle=Research on the influence of convex topography and overlying soil on the characteristics of strong ground motion, refAbstract=null), Reference(id=1245389889856975790, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389866096243586, doi=null, pmid=null, pmcid=null, year=1984, volume=3, issue=4, pageStart=174, pageEnd=183, url=null, language=null, rfNumber=[28], rfOrder=47, 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]. 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Value of parameter α in viscoelastic dynamic artificial boundary

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类型方向α取值
平面内法向2.0
二维人工边界平面内切向1.5
出平面切向0.5
), ArticleFig(id=1245389885159355177, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389866096243586, language=CN, label=表1, caption=

黏弹性动力人工边界中参数α的取值

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类型方向α取值
平面内法向2.0
二维人工边界平面内切向1.5
出平面切向0.5
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黏弹性人工边界的地震波参考波场选取方法比较分析
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宋贞霞 , 蒋永攀 , 丁海平
地震工程与工程振动 | 2024,44(2): 183-193
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地震工程与工程振动 | 2024, 44(2): 183-193
黏弹性人工边界的地震波参考波场选取方法比较分析
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宋贞霞 , 蒋永攀, 丁海平
作者信息
  • 苏州科技大学 江苏省结构工程重点实验室，江苏 苏州 215011

    • 宋贞霞（1979—），男，讲师，博士，主要从事地震工程和防灾减灾工程。E-mail：

通讯作者:

丁海平（1966—），男，教授，博士，主要从事地震工程和防灾减灾工程。E-mail：
Comparative analysis of seismic reference wave field selection methods based on viscoelastic artificial boundary
Zhenxia SONG , Yongpan JIANG, Haiping DING
Affiliations
  • Key Laboratory of Structural Engineering of Jiangsu Province, Suzhou University of Science and Technology, Suzhou 215011, China
doi: 10.13197/j.eeed.2024.0219
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摘要
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土-结构动力相互作用分析需要引入人工边界对无限域进行模拟，黏弹性人工边界是目前常用人工边界之一。在使用人工边界时，作为地震波动输入的地震波参考波场选取很关键，不同参考波场选取方法的计算精度有很大差异。假定均匀半空间、成层场地、凹陷地形和含地下结构等4种二维场地模型，采用ANSYS有限元软件结合黏弹性人工边界计算工具，考虑SV波垂直入射和30°倾斜入射2种情形，分别对采用3种不同参考波场输入的计算精度进行了详细比较，结果表明：当土-结构动力相互作用计算模型的所有人工边界均选用自由场作为参考波场时，计算结果精度最高。

土-结构动力相互作用  /  黏弹性人工边界  /  参考波场  /  二维场地  /  ANSYS

Artificial boundaries are introduced to simulate the infinite domain in the analysis of soil-structure dynamic interaction, and the viscoelastic artificial boundary is one of the commonly used artificial boundaries. When the artificial boundary is used, the selection of the reference wave field as the input of seismic wave is very important, different reference wave field selection methods will lead to great differences in calculation accuracy. In this paper, four kinds of two-dimensional site models, including homogeneous half space, layered site, depressed terrain and underground structure are assumed. Then ANSYS finite element software and viscoelastic artificial boundary are used to simulate the above four site models considering SV wave vertical incidence and 30° oblique incidence. The calculation accuracy of three different reference wave fields is compared in detail. The results show that when the free wave field is selected as the reference wave field for all artificial boundaries of the soil-structure dynamic interaction calculation model, the accuracy of the calculation results is the highest.

soil-structure dynamic interaction  /  viscoelastic artificial boundary  /  reference wave field  /  two dimensional field  /  ANSYS
宋贞霞, 蒋永攀, 丁海平. 黏弹性人工边界的地震波参考波场选取方法比较分析. 地震工程与工程振动, 2024 , 44 (2) : 183 -193 . DOI: 10.13197/j.eeed.2024.0219
Zhenxia SONG, Yongpan JIANG, Haiping DING. Comparative analysis of seismic reference wave field selection methods based on viscoelastic artificial boundary[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (2) : 183 -193 . DOI: 10.13197/j.eeed.2024.0219
正文
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0　引言
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土-结构动力相互作用分析需要引入人工边界对无限域进行模拟，常用的人工边界有黏性边界[1]、黏弹性边界[2]、旁轴边界[3]、一致边界[4]、透射边界[5]等。相对而言，黏弹性人工边界具备概念清晰，稳定性高，精度较好等特点，易于应用。刘晶波等[6]将黏弹性人工边界与大型有限元结构分析软件结合，同时还给出一种新的地震波输入方法，即把地震波转化为模型网格节点上的等效节点力，可模拟波动入射过程而又不影响人工边界处理散射波的精度，发展并推广了结构-地基动力相互作用问题的直接分析方法[7-9]。在应用黏弹性人工边界过程中，如何正确模拟地震波动输入是关键问题之一[10]。由于在人工边界上模拟地震波输入和辐射阻尼作用是近似的，人工边界上选取的参考波场精度越高，场地地震响应模拟的精度也越高。
地震波动的输入参考波场一般作为已知条件，不同研究人员选取方法并不一致，既可以选用场地中的自由场，也可以选用入射场。针对均匀半空间场地，部分研究人员如杜修力等[11-12]、汪精河等[13-14]和孙纬宇等[15]认为在基于黏弹性人工边界考虑地震波输入时，底边界输入入射场，左侧边界输入自由场，右侧边界无波场输入。另一部分研究人员如章小龙等[16]认为底边界可采用入射场，左、右侧边界应输入自由场。而赵源等[17]、黄景琦[18]、李明超等[19]和SONG等[20]则建议底边界、左侧边界和右侧边界均应采用自由场作为参考波场。针对这3种不同参考波场选取方式，张梁等[21]采用波场分离的方法比较了P波倾斜入射下二维弹性半空间的计算精度；王飞等[22]同样采用波场分离法比较了SV波倾斜入射三维弹性半空间的计算精度，结果表明各人工边界均考虑自由场输入时，计算值与理论值吻合度最高。由于上述场地模型是均匀半空间，参考波场均采用波场分离法计算，对于水平成层场地和包含散射体场地模型的自由场分析，难以追踪复杂的反射波和透射波，用波场分离法求解较为困难。本文将根据传递矩阵法计算自由场作为参考波场，通过线弹性本构矩阵结合动力平衡方程计算节点应力，实现地震波动输入。黏弹性人工边界假定3种输入方法：第一种方法为左侧边界输入自由场，底部边界输入入射场，右侧边界不考虑输入；第二种方法为左、右侧边界输入自由场，底部边界输入入射场；第三种方法为左、右侧边界和底部边界均输入自由场。分别采用上述3种输入方法计算SV波斜入射下均匀半空间、成层场地、不规则场地（凹陷地形）和含有地下结构场地的地震响应，详细比较人工边界采用不同参考波场输入的计算精度。当地震波垂直入射时，左、右侧边界的参考波场是一致的，均采用自由场，只比较第二种和第三种方法计算精度。
1　黏弹性人工边界实现方法
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1.1　黏弹性人工边界参数选取
黏弹性人工边界条件可以等效为在人工截断边界上设置连续分布的并联弹簧-阻尼器系统，其中弹簧元件的弹性系数Kb和黏性阻尼器的阻尼系数Cb的计算公式为[23]
式中：ρ和G分别为介质的质量密度和剪切模量；rb为散射波源到人工边界的距离；c为介质中的波速，法向人工边界取P波波速cp，切向人工边界取S波波速cs；参数α根据人工边界的类型及设置方向取值，如表1所示。
1.2　等效节点力计算
针对黏弹性边界，刘晶波等[6]将输入地震动转化为作用在人工边界上的等效节点力，人工边界上的输入位移和应力与原自由场的相同。等效节点力公式为
式中：Fi为黏弹性边界上节点等效力；Ki和Ci分别为弹簧刚度矩阵和阻尼矩阵；ui、和σi分别是人工边界i节点的位移、速度和表面应力向量；Ai为边界i节点的控制面积，对于规则的等距边界单元，等于单元边界线长度的1/2，如图1所示。图1中KN和CN分别为法向弹簧和法向阻尼；KT和CT分别为切向弹簧和切向阻尼。
模型中边界上每个节点的位移时程和速度时程均已知，应力时程则可通过线弹性本构矩阵结合动力平衡方程，利用有限元进行空间离散，把动力平衡方程转化为等效积分形式，最后再结合Snell定律进行空间一维化，即可推导出节点应力表达式[24-27]。
1.3　黏弹性人工边界在ANSYS中的实现
本文通过ANSYS有限元分析软件APDL语言进行二次开发，采用combine14单元，根据式（1）和表1中内容计算弹簧和阻尼系数并编写黏弹性边界施加命令，将单元批量施加在土体模型边界节点处。弹簧和阻尼器在边界节点处施加形式如图1所示。根据人工边界等效节点力3种方法具体计算公式编写添加节点等效力命令，实现边界节点处批量施加黏弹性边界和等效节点力。
2　参考波场选取方法和验证
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2.1　参考波场
在构建边界节点的等效力方程时，需要利用参考波场。边界区域内参考波场既可选择自由场作为参考波场，也可选择入射场作为参考波场。所谓自由场，是指当广义结构不存在时入射波在无限域中产生的波场，包含入射波和土层界面反射波。当无限域较简单时（例如，均匀弹性半空间），自由场有解析表达式，如可通过波场分离法计算得到。当无限域较复杂时（如成层弹性半空间），自由场可以基于传递矩阵法预先计算得到，并以文件形式保存。
本文以SV波从二维均匀半空间左下方斜入射为例，如图2所示，其中入射波和左边界的夹角α代表入射角度，采用波场分离法可以直观地反映3种参考波场的选取方法：方法1，左边界输入为自由场，底边界输入为入射场，右边界不考虑如图2（a）所示；方法2，左边界输入为自由场，底边界输入为入射场，右边界输入为自由场如图2（b）所示；方法3，左边界、底边界和右边界输入均为自由场如图2（c）所示。
根据式（2），有3种不同输入方法的等效节点力表达式。
1）方法1
左边界等效力公式为
底边界等效力公式为
右边界等效力公式为
2）方法2
左边界等效力公式为
底边界等效力公式为
右边界等效力公式为
3）方法3
左边界等效力公式为
底边界等效力公式为
右边界等效力公式为
式中：和分别为i节点处自由场的位移和速度；、分别为i节点处入射场的位移和速度；和分别为i节点处根据自由场数据计算出的正应力和剪应力；和分别为i节点处根据入射场数据计算出的正应力和剪应力；Ai为边界i节点控制面积。
2.2　算例验证
建立二维均匀半空间场地如图3所示，尺寸均为100 m×50 m，土体参数如图中所示，图中ρ为土的密度，ν为泊松比，cs为剪切波速。单元计算尺寸dx =dy =0.5 m，考虑SV波垂直入射和30°倾斜入射2种情形，入射波形如图4所示，脉冲宽度为0.2 s，时间步长dt =0.001 s。在场地中设置6个监测点，分别为点1（0，50），点2（50，50），点3（100，50），点4（50，25），点5（0，0）和点6（100，0）。同理，建立二维成层场地如图5所示。详细比较黏弹性人工边界3种不同的参考波场输入方法计算值与理论值的差异，其中理论值是根据传递矩阵法得到。
位移时程图中的AR标明了人工边界反射波的到达时刻，可以详细比较分析误差的产生。其中AR指向的时刻可以按最短路径（从源到最近的人工边界，再返回到监测点）除以波速进行估算[28]。AR1表示参考波场输入计算区域，到达地表反射后穿透底部人工边界时引起的误差经最短路径传播到各监测点的到达时刻。AR2表示参考波场（斜入射情形）输入计算区域，到达右侧人工边界时引起的误差经最短路径传播到各监测点的到达时刻。
SV波垂直入射各监测点水平方向位移时程如图6所示。对于垂直入射，只比较方法2和方法3。由图可知，方法3的计算结果与理论值一致，方法2的结果存在一定误差，且底部产生误差的时刻先于地表误差出现的时刻。地震波从地表反射至底部人工边界的时刻AR1为0.5 s，从监测点5和监测点6可以观察到此时刻方法2首先开始出现误差，监测点4在0.625 s出现误差波，而监测点1~3的误差波到达时间AR1都为0.75 s。
SV波30°斜入射时各监测点水平方向的位移时程线如图7所示。地震波从地表反射至底部人工边界的时刻AR1为0.3 s，从监测点5可以观察到此时刻方法2首先开始出现误差，监测点1、4、2、6和3的误差波到达时刻AR1依次为0.444、0.461、0.504、0.55、0.632 s。右侧边界出现误差最早到时AR2为0.25 s，从监测点6可以观察到此时刻方法1首先开始出现误差，该误差波在监测点1~5的到达时刻AR2分别为0.573、0.454、0.394、0.411、0.539 s。二维均匀半空间场地中方法3精度高于方法2，方法2精度比方法1高。
SV波垂直入射成层场地各监测点水平方向的位移时程如图8所示。同样只比较方法2和方法3的计算精度。从监测点5、6可以观察到AR1（0.15 s）时刻方法2首先开始出现误差，监测点4在0.189 s出现误差波，而监测点1~3的误差波到时AR1都为0.224 s。
SV波30°斜入射时各监测点水平方向的位移时程如图9所示，从监测点5可以观察到AR1（0.07 s）时刻方法2计算结果开始出现误差，监测点4、1、6、2、3的误差波到时AR1依次为0.109、0.11、0.112、0.119、0.148 s。右侧边界误差波最早到时AR2为0.042 s，可以首先从监测点6观察到方法1精度开始下降，该误差波在监测点1~5的到时AR2分别为0.12、0.091、0.077、0.081、0.09 s。3种不同地震动输入方法在二维成层场地中计算结果精度同样存在差异，方法3精度高于方法2和方法1。
位移场云图较位移时程曲线可以更为直观地观察出入射波在土体中的传播和波经过人工边界时的透射反射过程。由于成层场地每层土体参数不同，土体分界面引起入射波多次反射折射导致云图图像呈现不规则状态，因此本文选用均匀半空间场地位移场云图。SV波30°斜入射进入土体时3种不同方法在相同时刻的位移场云图如图10所示，其中图10（a）、（b）、（c）为采用方法1时0.25、0.45、0.60 s这3个时刻的位移场云图，图10（d）、（e）、（f）为采用方法2时3个时刻的位移场云图，图10（g）、（h）、（i）为采用方法3时3个时刻的位移场云图。0.25 s时刻3种方法的云图图像显示相同，图7所示各监测点3种方法此时刻的位移时程曲线基本吻合。与方法2相比，方法1未考虑右边界的地震动输入，方法3底部采用自由场输入，从0.45 s的位移云图可以观察到方法1、方法2和方法3在云图的右侧出现明显差异，方法1、方法2和方法3云图在底部出现差异。误差刚出现时从位移时程曲线图上难以体现，但云图却可清晰表现出来。
3　含散射源场地地震响应分析
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根据对二维均匀半空间场地和成层场地3种参考波场选取方法的计算精度分析可得，方法3的精度最高，但对包含散射源地形的场地，当入射波接触到散射源时会产生复杂且难以追踪的反射波，对计算精度有显著影响，本文下面对含散射源的地形场地进行分析。建立长100 m，高50 m的二维土体模型，土体材料参数同二维均匀半空间场地算例。分别从基底垂直入射和以30°倾角入射SV波，入射波形如图4所示。假定包含2种不同散射源研究参考波场选取方法对计算精度影响，将远置边界的数值解作为理论值与计算结果进行比较分析。
1）二维凹陷地形场地，其中半圆凹陷处半径R = 10 m，如图11所示。设置了6个监测点，分别为点1（10，50）、点2（30，50）、点3（40，50）、点4（42，44）、点5（50，40）和点6（60，50）。
2）二维地下结构场地，如图12所示。其中地铁结构高8 m，宽20 m，中柱宽1 m，边墙厚1 m，顶底板厚1 m，顶板埋深5 m。地铁车站结构为钢筋混凝土材料构成，混凝土的弹性模量为E = 35×109 Pa，泊松比v =0.15，重度为24.50 kN/m3，中柱的弹性模量为0.86×109 Pa。计算单元尺寸为dx =dy =0.5 m。在模型中设置了6个监测点，分别为点1（41，50），点2（50，50），点3（59，50），点4（50，44），点5（41，38）和点6（59，38）。
凹陷场地SV波垂直入射和30°斜入射各监测点水平方向位移时程曲线分别如图13和图14所示，监测点1~点6为方法2的计算结果，在AR1时刻较方法3开始出现误差，但总体误差不大。在AR2时刻方法1较方法2精度开始下降。方法2和方法3精度明显高于方法1，方法3精度略高于方法2。地下结构场地SV波垂直入射和30°斜入射各监测点水平方向位移时程曲线分别如图15和图16所示。3种方法计算结果分析结论与凹陷场地类似，方法3精度最高。
4　结论
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本文总结了3种常见参考波场选取方法，并以SV波垂直入射和斜入射下分析比较了均匀半空间、成层场地、不规则地形（凹陷场地）和含地下结构的4种场地的不同参考波场输入方法的计算精度，得出以下结论：
1）左边界、底边界和右边界输入均采用自由场的计算精度最高；左、右边界输入采用自由场，底边界输入为入射场的精度次之；左边界输入采用自由场，底边界输入为入射场，右边界不考虑输入时的误差最大。
2）对于所有的计算模型，当地震波垂直输入时，第三种方法的精度稍高于第二种方法，但地震波斜入射时，第三种方法的精度明显高于第一种和第二种方法。
3）当考虑P波入射时，亦得到上述结论。
综上，建议土-结构动力相互作用分析选择黏弹性边界作为人工边界时，所有人工边界的波动输入均宜采用自由场作为参考波场。
基金
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  • 国家自然科学基金项目(51808371)
文献
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2024年第44卷第2期
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doi: 10.13197/j.eeed.2024.0219
  • 接收时间：2022-12-13
  • 首发时间：2026-03-30
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  • 收稿日期：2022-12-13
  • 修回日期：2023-05-17
基金
国家自然科学基金项目(51808371)
作者信息
    苏州科技大学 江苏省结构工程重点实验室，江苏 苏州 215011

通讯作者:

丁海平（1966—），男，教授，博士，主要从事地震工程和防灾减灾工程。E-mail：
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