Article(id=1228654094957609629, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228654089437901468, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.12.007, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1668700800000, receivedDateStr=2022-11-18, revisedDate=1677168000000, revisedDateStr=2023-02-24, acceptedDate=null, acceptedDateStr=null, onlineDate=1770863563526, onlineDateStr=2026-02-12, pubDate=1735315200000, pubDateStr=2024-12-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770863563526, onlineIssueDateStr=2026-02-12, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770863563526, creator=13701087609, updateTime=1770863563526, updator=13701087609, issue=Issue{id=1228654089437901468, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='12', pageStart='1993', pageEnd='2167', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770863562211, creator=13701087609, updateTime=1770863940325, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228655675413299456, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228654089437901468, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228655675413299457, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228654089437901468, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=2055, endPage=2065, ext={EN=ArticleExt(id=1228654096605971104, articleId=1228654094957609629, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Effect of overlying crust on seismic response of inclined liquefiable site-pile foundation-structure system, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The seismic dynamic response of pile foundation in inclined liquefaction site is an important issue in the field of geotechnical seismic engineering. Based on the shaking table model test carried out by our research group and the OpenSees software platform,a two-dimensional integrated numerical model of inclined liquefied soil-pile group-structure interaction is established in this paper. The nonlinearity of pile-soil contact and the shear localization of soil layer are considered in the model. The rationality and effectiveness of the numerical simulation method are verified by comparing with the shaking table test results. On this basis,a typical inclined liquefied site-pile group-structure interaction finite element model is established to discuss the influence of different overlying crust on the seismic response of site and structure system. The calculation results show that with the increase of the thickness of overlying crust,the pore pressure ratio in the saturated sand decreases,the horizontal residual displacement of soil decreases,and the displacement of pile body and the pile curvature decrease. The effect of the strength of overlying crust on the dynamic response of pile foundation is more obvious. The increase of the thickness of overlying crust can reduce the liquefaction degree of sand and improve the mechanical performance of pile foundation.

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倾斜液化场地桩基的地震动力响应是岩土抗震工程领域关注的重要问题。本文依据振动台模型试验,基于OpenSees软件平台建立了倾斜液化场地-群桩-结构相互作用二维整体化数值模型,模型中考虑了桩-土接触的非线性以及土层的剪切局部化,并通过与振动台试验结果进行对比,验证了本文数值模拟方法的合理性和有效性。在此基础上,建立了针对实际场地的典型倾斜液化场地-群桩-结构相互作用有限元模型,讨论了不同上覆土层参数对场地及结构体系地震反应的影响。计算结果表明:随着上覆土层厚度的增大,饱和砂土层中的孔压比减小,土体的水平残余位移减小,同时桩身位移以及桩基曲率均有所减小;上覆土层强度对桩基动力反应的影响更加显著;上覆土层厚度的增加可以降低土层的液化程度并提高桩基的受力性能。

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张小玲(1980—),女,博士,教授。电话: (010)69391980; E-mail:

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张小玲(1980—),女,博士,教授。电话: (010)69391980; E-mail:

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张小玲(1980—),女,博士,教授。电话: (010)69391980; E-mail:

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Model material parameters

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参数砂土层黏土层
密度ρ/(g⋅cm-3)1.71.7
参考剪切模量Gr/kPa60000150000
参考体积模量Br/kPa160000750000
摩擦角ɸ/(°)310
八面体峰值应γmax0.10.1
参考围压pr/kPa101101
压力系数 np0.50.5
相位角 ɸPT/(°)31
剪缩参数 c10.093
剪缩参数 c30.18
剪胀参数 d10.0
剪胀参数 d20.17
黏聚力c/kPa75
屈服面数n2020
), ArticleFig(id=1228654111235702960, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228654094957609629, language=CN, label=表1, caption=

模型材料参数

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参数砂土层黏土层
密度ρ/(g⋅cm-3)1.71.7
参考剪切模量Gr/kPa60000150000
参考体积模量Br/kPa160000750000
摩擦角ɸ/(°)310
八面体峰值应γmax0.10.1
参考围压pr/kPa101101
压力系数 np0.50.5
相位角 ɸPT/(°)31
剪缩参数 c10.093
剪缩参数 c30.18
剪胀参数 d10.0
剪胀参数 d20.17
黏聚力c/kPa75
屈服面数n2020
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上覆土层对倾斜液化场地-桩基-结构地震反应的影响研究
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张小玲 1, 2 , 房丽净 1, 2 , 许成顺 1, 2 , 贾科敏 1, 2
振动工程学报 | 2024,37(12): 2055-2065
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振动工程学报 | 2024, 37(12): 2055-2065
上覆土层对倾斜液化场地-桩基-结构地震反应的影响研究
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张小玲1, 2 , 房丽净1, 2, 许成顺1, 2, 贾科敏1, 2
作者信息
  • 1北京工业大学建筑工程学院,北京 100124
  • 2北京工业大学城市与工程安全减灾教育部重点实验室,北京 100124
  • 张小玲(1980—),女,博士,教授。电话: (010)69391980; E-mail:

Effect of overlying crust on seismic response of inclined liquefiable site-pile foundation-structure system
Xiao-ling ZHANG1, 2 , Li-jing FANG1, 2, Cheng-shun XU1, 2, Ke-min JIA1, 2
Affiliations
  • 1College of Architecture and Civil Engineering,Beijing University of Technology,Beijing 100124,China
  • 2Key Laboratory of Urban Security and Disaster Engineering,Ministry of Education,Beijing University of Technology,Beijing 100124,China
出版时间: 2024-12-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.12.007
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倾斜液化场地桩基的地震动力响应是岩土抗震工程领域关注的重要问题。本文依据振动台模型试验,基于OpenSees软件平台建立了倾斜液化场地-群桩-结构相互作用二维整体化数值模型,模型中考虑了桩-土接触的非线性以及土层的剪切局部化,并通过与振动台试验结果进行对比,验证了本文数值模拟方法的合理性和有效性。在此基础上,建立了针对实际场地的典型倾斜液化场地-群桩-结构相互作用有限元模型,讨论了不同上覆土层参数对场地及结构体系地震反应的影响。计算结果表明:随着上覆土层厚度的增大,饱和砂土层中的孔压比减小,土体的水平残余位移减小,同时桩身位移以及桩基曲率均有所减小;上覆土层强度对桩基动力反应的影响更加显著;上覆土层厚度的增加可以降低土层的液化程度并提高桩基的受力性能。

地震响应  /  桩-土相互作用  /  上覆土层  /  倾斜液化场地  /  数值模拟

The seismic dynamic response of pile foundation in inclined liquefaction site is an important issue in the field of geotechnical seismic engineering. Based on the shaking table model test carried out by our research group and the OpenSees software platform,a two-dimensional integrated numerical model of inclined liquefied soil-pile group-structure interaction is established in this paper. The nonlinearity of pile-soil contact and the shear localization of soil layer are considered in the model. The rationality and effectiveness of the numerical simulation method are verified by comparing with the shaking table test results. On this basis,a typical inclined liquefied site-pile group-structure interaction finite element model is established to discuss the influence of different overlying crust on the seismic response of site and structure system. The calculation results show that with the increase of the thickness of overlying crust,the pore pressure ratio in the saturated sand decreases,the horizontal residual displacement of soil decreases,and the displacement of pile body and the pile curvature decrease. The effect of the strength of overlying crust on the dynamic response of pile foundation is more obvious. The increase of the thickness of overlying crust can reduce the liquefaction degree of sand and improve the mechanical performance of pile foundation.

seismic response  /  pile-soil interaction  /  overlying crust  /  inclined liquefiable site  /  numerical simulation
张小玲, 房丽净, 许成顺, 贾科敏. 上覆土层对倾斜液化场地-桩基-结构地震反应的影响研究. 振动工程学报, 2024 , 37 (12) : 2055 -2065 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.12.007
Xiao-ling ZHANG, Li-jing FANG, Cheng-shun XU, Ke-min JIA. Effect of overlying crust on seismic response of inclined liquefiable site-pile foundation-structure system[J]. Journal of Vibration Engineering, 2024 , 37 (12) : 2055 -2065 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.12.007
桩基础是在岩土工程中常见的基础形式,因其有良好的工程特性和抗震性能而在工程界得到广泛的应用。然而近年来多次地震震害表明,在具有显著液化潜力的液化侧向扩展场地中,桩基础易发生破坏,进而引发上部结构的失效1。如1964年日本新潟地震和美国阿拉斯加地震、1976年中国唐山地震、1995年的日本神户地震和2011年新西兰地震等均出现液化场地侧向扩展导致桩基础破坏的案例2。针对这一问题国内外众多学者通过模型试验、数值模拟等手段开展了大量研究。
振动台模型试验和离心机模型试验是目前关于液化场地桩-土相互作用研究中最常见的试验方法。CUBRINOVSKI等3采用大型层状剪切箱,基于液化侧向扩展大型振动台试验,研究了侧向扩展条件下桩基的力学特性及液化土层极限侧向位移响应。EBEIDO等4报道了单桩和群桩基础在液化侧向扩展作用下的动力反应,通过水位线高度的变化来研究上覆非液化土层在液化侧向扩展场地中对桩基础动力反应的影响。WANG等5基于振动台试验对比分析了水平场地中完全上覆非液化土层、部分上覆非液化土层、无上覆黏土层中群桩基础-桥墩-上部结构体系的动力响应,讨论了冲刷对桩基础破坏的影响。王志华等6考虑附加质量块、底部嵌固条件以及长径比等因素,开展了水平和倾斜液化地基单桩振动台模型试验,研究了液化土体侧向扩展效应对单桩动力反应的影响。TANG等7针对液化侧扩流场地桩-土相互作用开展了振动台模型试验研究,通过试验得到了作用在桩基上的液化侧向土压力大小。汪明武等8通过离心机试验研究了倾斜液化场地群桩基础的地震响应特征,分析了强震条件下群桩基础的变形特性和液化场地侧向流动性能,研究了桩基的破坏机理。
相比物理模型试验周期长、费用高、过程中条件难以控制等困难,数值模拟方法能够在较短时间内对液化场地进行水-土耦合分析,模拟饱和土体的剪缩、剪胀等液化特性,更方便获取土和结构的动力响应1。ELGAMAL等9基于OpenSees平台建立了多屈服面弹塑性本构模型,并基于试验对本构模型参数进行了标定,该本构模型能够较好描述饱和砂土的液化特性。CHANG等10借助OpenSees有限元平台,采用与有效应力和总应力有关的塑性本构模型模拟饱和砂土和黏土,考虑饱和砂土的液化特性,以弹簧模拟桩-土接触非线性,建立液化侧向扩展场地土-群桩基础-上部结构二维非线性有限元模型,将计算结果和试验结果进行对比,验证了模型的可靠性。王晓伟等11基于OpenSees有限元模型,建立了典型河谷场地三跨简支梁模型,分析了各部件在液化侧向扩展场地中的地震动力响应。林大富等12研究上覆土层厚度及土体塑性指数对地震作用下的可液化场地响应的影响。张效禹等13通过建立液化场地桩-土动力相互作用三维有限元数值模型,研究了砂土的渗透系数、内摩擦角和相对密度、上覆黏土层厚度及桩径对p-y曲线的影响效应。崔杰等14建立液化微倾场地群桩-土动力相互作用有限元模型,系统研究了场地倾斜角度、桩径、地震作用幅值和基桩位置对饱和砂土动力p-y曲线特性的影响。孙艳国等15基于有限元软件ABAQUS,建立不同厚度的上覆软黏土层场地中桩-筒复合基础数值分析模型,考虑不同荷载作用下上覆软黏土层厚度对桩-筒复合基础的影响,研究认为海上风电桩-筒复合基础的设计应充分考虑上覆软黏土层对桩-筒复合基础承载特性的影响。
综上,目前针对液化场地中桩-土相互作用问题的研究中,大多关注桩基破坏机理及考虑多种因素对桩基动力响应的影响,而针对桩基动力响应的影响因素分析也主要集中在液化土、桩、结构尺寸等方面,对上覆非液化土层的关注相对较少。由于实际场地中大多存在上覆土层,且实际工程中也均有为防止地基土液化而进行人工回填的上覆土层,而倾斜液化场地的液化土体会同时带动上覆土层发生侧向扩展从而加大对结构的破坏,所以有必要针对上覆土层对倾斜液化场地-桩基-结构动力响应的影响进行研究。
本文结合前期完成的振动台试验,基于Open- Sees开源有限元计算平台建立了倾斜液化场地-群桩-结构相互作用二维整体化数值模型。通过与振动台模型试验结果的对比,验证了数值模拟方法的合理性。在此基础上,针对实际建立典型倾斜液化场地-群桩-结构体系相互作用数值模型,讨论了上覆土层对体系地震反应的影响。
开展的液化侧向扩展场地-群桩基础-上部结构体系的大型振动台试验在中国建筑科学研究院抗震实验室完成。试验采用净尺寸为3.2 m×2.4 m×2.2 m(长×宽×高)的层状剪切模型箱,在模型箱底部采用倾斜角度为2°的钢筋混凝土底座模拟场地倾斜的条件,振动台试验物理模型如图1所示16。振动台试验中对土体的孔压、加速度、位移以及桩身曲率等进行测量,传感器整体布置如图2所示。
振动台模型试验中土层厚度为2 m,自上而下为0.3 m上覆硬土层,1.7 m饱和砂土层,水位线与饱和砂土层上游边界保持一致。试验中采用2×2布置的高承台钢筋混凝土群桩,桩基直径为0.1 m,高度为1.9 m,桩中心间距为0.4 m,桩基配备6根6 mm的纵筋,保护层厚度为1 cm;桥墩直径为0.2 m,高度为1 m,配备10根10 mm的纵筋,保护层厚度为2 cm;上部结构配重质量为1.6 t的铅块;承台被设计为0.7 m×0.7 m×0.3 m的钢筋混凝土试件。桩头与承台、墩柱与承台均为刚性连接,桩端固定在模型箱底部以此来模拟实际场地中的坚硬土层。
试验中选用Tabas地震记录为主要输入地震动,加速度峰值为0.3g,其时程曲线如图3所示。
根据前期完成的振动台试验,本文基于Open- Sees开源有限元计算平台建立了倾斜液化场地群桩-土体-结构相互作用二维整体化数值模型,如图4所示,具体建模过程如下。
在本文的数值模拟中,地基土中的饱和砂土层和上覆硬土层均采用二维四边形平面应变单元quadUP17模拟,quadUP单元是基于Biot土-水耦合作用理论开发的土体单元,单元包含土体水平位移、竖向位移以及孔隙水压力三个自由度,在土体液化分析中可以较好地模拟饱和砂土与水的动力耦合作用机制。
对于饱和砂土,采用对围压变化较为敏感的多屈服面塑性本构模型,在OpenSees计算平台中选取对应的PressureDependMutiYield02本构模型18,可模拟砂土在循环荷载作用下出现的剪胀流动等现象且考虑了液化引起的砂土永久剪应变循环累积效应;对于黏土,选用对围压变化不敏感的多屈服面本构模型,在OpenSees中选取对应的PressureIndependMutiYield本构模型19,可以更好地模拟黏土的剪切弹塑性特征;模型的参数主要是根据振动台试验中试验条件16并结合OpenSees官网推荐19进行取值。饱和砂土和黏土的具体的材料参数取值如表1所示。
本文数值模拟中考虑桩基和墩柱的非线性特性,采用Dispbeamcloumn19单元对桩基和墩柱单元进行模拟,对二者的纤维截面均采用Section fiber19截面进行模拟;桩基和上部结构中的混凝土和钢筋的材料分别选用OpenSees中推荐的Concrete01材料和Steel02材料。承台的模拟采用OpenSees中Quad19单元及弹性材料本构模型进行模拟。上部结构简化为质量点施加在桥墩顶部;桩与承台、承台与桥墩均采用刚性连接,以此模拟振动台模型试验中承台对桩基和桥墩的嵌固作用。
为了更好地模拟倾斜液化场地桩-土相互作用中的接触非线性,数值建模中分别采用p-yt-z弹簧考虑桩身与土体的侧向、竖向的相互作用。由于模型试验中桩端固定在模型箱底部,故不考虑桩端与土体的竖向相互作用。本文数值模拟所采用的桩-土相互作用模型如图5所示。
在饱和砂土层中桩-土相互作用的模拟中,采用考虑液化效应的p-yt-z弹簧来考虑桩身与饱和砂土的侧向、竖向相互作用,相应的选取OpenSees中的PyLiq1,TzLiq1本构模型作为桩土相互作用接触的本构模型。
其中,在上述PyLiq1,TzLiq1本构模型中,考虑饱和砂土液化的极限强度pult,liq,tult,liq可表示为:
式中  pulttult为土体未液化时侧向、竖向的极限强度;press为土体液化后的极限强度,采用press=pultmp来计算,其中系数mp可根据BRANDENBERG等20推荐得到;ru为土体超孔隙水压力比。
其中,饱和砂土p-y弹簧模型中的土体侧向的极限强度pult可根据API规范21来确定,如下式所示:
最终的可液化砂土的桩周土抗力计算公式,即可液化砂土的p-y关系式由下式表示:
式中  C1C2C3为随土体内摩擦角变化的系数;D为桩径;γ为土体有效重度;A为荷载系数,若为循环荷载,则A取0.9;z为泥面以下某点桩的深度;y表示土体侧向位移;nh为地基反力模量系数,本文基于BOULANGER等22的研究考虑土体上覆有效应力对地基反力模量的影响,采用相关参数对不同深度处nh进行修正。
饱和砂土t-z弹簧中的极限强度tult可根据API规范21由下式计算得到:
可液化砂土的t-z弹簧关系式由下式21表示:
式中  K0为土压力系数,一般取0.4;σv΄为土体竖向有效应力;δ为桩-土之间内摩擦角,一般取土体内摩擦角的0.8倍;P为桩的周长;zc为桩-土竖向相互作用力达到极限时对应的竖向位移临界值。
黏土层中的桩-土相互作用采用不考虑土体液化的PySimple1,TzSimple1弹簧本构模型来模拟桩身与土体的侧向、竖向相互作用。
其中,黏土层中的p-y弹簧的极限强度pult可根据API规范21得到,黏土的p-y曲线关系式可由下式来表示:
式中  cu为黏土的不排水剪切强度;J为土体黏稠系数,一般取0.25~0.5;ɛ50为土体极限应力的50%对应的应变,对于软黏土、中黏土和硬黏土分别取为0.02,0.01和0.005。
黏土层的t-z弹簧关系式与可液化砂土的相一致(见式(6)),但计算时需将公式中的tult,liq改为tult,ctult,c可由下式21计算得到:
式中  αt为桩侧摩阻力无纲量系数,通常取为0.1;B为桩截面面积。
在振动台模型试验中,由于上覆黏土层的渗透系数比较低,当中间饱和砂土层发生液化时,砂土层顶面土体中的孔隙水来不及排出,从而在砂土层顶层土体与上覆黏土层之间形成一层结合水膜,使该处土体的抗剪强度降低,导致黏土层与饱和砂土层交界处在地震激励下产生振荡和位移不连续,即所谓的液化松散砂层与非液化黏土层间的剪切局部化。
本文为了模拟这种剪切局部化的现象,基于WANG等23提出的运用OpenSees中的土壤材料库的简化建模技术,在上覆黏土层与饱和砂土层交界处设置厚度为hw和相应的低参考剪切模量Gr,soft软层间单元,该层间土体单元的其他材料参数与饱和砂土单元相同,但其中软层间单元的低参考剪切模量Gr,soft取决于层厚hw,二者的关系如下式所示:
式中  hw表示由于黏土层内部或底部水膜的形成而引起的剪切局部化范围,根据已有的试验研究总结发现,hw一般在0.1~0.9 m23;本文的数值模拟中选取hw为0.1 m。值得注意的是,该方法只适用于可液化土层上覆有非液化土层,从而导致有侧向扩展发生的缓坡场地。对于坡度较大的土体场地,在使用该方程时会引起较大的误差。
本文的数值模型中,采用等效自由度约束的方法将模型两侧同一高度土体的水平、竖直方向位移自由度绑定来建立剪切边界条件1324,这样模型两侧同一高度处的土体,其水平竖直两个方向位移分别一致,实现了两侧土体协同变形,以此来模拟振动台试验中土体的剪切变形。同时将模型底部土体的位移自由度进行约束来模拟下部坚硬土层,土体模型的底部和侧边界均设置成不排水边界。在数值模拟过程中采用基于位移的收敛准则。为模拟土体的动力非线性和耗能能力,参考相关研究成果24在模型中设置瑞利阻尼,阻尼比取为0.03。
在对倾斜液化场地-群桩-结构体系进行加载时,首先将土体设置为弹性状态,将土体渗透系数设置为1 m/s,然后进行自重应力分析得到初始应力场;接着加入结构和桩-土连接弹簧,并将弹簧设置为弹性状态进行自重应力分析,从而得到加结构体系后的初始应力场;最后将土体的渗透系数更改为实际值,将土体、结构材料以及桩-土连接弹簧设置为塑性状态,采用一致激励的方式进行动力分析。
为了验证本文所建立的数值模型的有效性,将本文所建立的数值模型计算得到的土体的超孔压比、加速度、位移以及桩身曲率与前期开展的振动台模型试验结果进行对比。
图6给出了本文数值模拟和模型试验中不同土体深度处的孔压比时程结果的对比情况,可以看出本文对孔隙水压力的模拟结果与模型试验结果趋势基本一致。在孔压发展的第一阶段(0~5 s),由于输入的地震动加速度幅值较小,超孔隙水压力均未开始发展;在第二阶段(5~12 s),随着基底输入的地震动加速度的幅值逐渐增大并达到峰值,土体的超孔隙水压力快速累积直至部分土体达到液化;在第三阶段(12~40 s),输入地震动加速度的幅值逐渐减弱,在此阶段土体中的孔隙水压力逐渐开始消散。图6中的第二阶段(5~12 s),相比模型试验的结果,数值模拟结果中的孔隙水压力增长速度较快,可能是因为模型试验中存在模型箱的耗能以及所选用的quadUP土体单元没有考虑土体自身加速度的影响25。在第三阶段(12~40 s)土体孔压消散程度有一定的差异,尤其是饱和砂土顶层,分析其原因可能是因为模型试验中土体的渗透系数分布不均匀以及测点布置精准程度等因素导致24
从总体上看,本文数值模拟得到的孔隙水压力发展趋势与模型试验结果基本一致,因此可认为本文所建立的数值模型较好地再现了倾斜液化场地-桩基-结构中饱和砂土层的孔隙水压力动力反应。
图7给出了本文数值模拟的结果与模型试验中不同深度处土体的加速度时程曲线和加速度峰值曲线的对比情况,由图7(a)可以看出不同深度处土体加速度的数值模拟结果和模型试验结果吻合较好。同时由图7(b)可以看出,在饱和砂土层中随着土体埋深的增大,土体加速度峰值逐渐减小,说明土体液化后具有通低频滤高频的效果,这与其他文献结论基本一致824图7(b)中加速度的峰值在黏土层出现突变,这可能是由于饱和砂土层地震液化后土体刚度降低,从而使得与黏土层的刚度差异增大导致的。图7(b)中土体水平加速度峰值的模拟结果和试验结果在砂土层的部分测点有一定差异,分析其原因主要是由于本文的数值模拟中没有考虑模型箱耗能的影响。
图8给出了场地土的水平残余位移沿深度变化的数值模拟结果与模型试验结果的对比情况,可以看出两个结果沿着深度的变化趋势基本一致。随着埋深的减小,饱和砂土层土体的水平残余位移逐渐增大,到达黏土层后位移又出现减小的趋势,最大的土体水平残余位移出现在饱和砂土层与黏土层交界面处,达到了31.9 mm,并且该处出现了位移突变现象,这也说明了考虑不同土体交界面的剪切局部化的数值模型的合理性。相比交界面处的土体位移,黏土层的位移相对较小,这是因为上覆黏土层不透水,因此在黏土与饱和砂土层界面处积聚了大量的孔隙水,降低了交界面处的摩擦力,使得砂土层无法更好地带动上覆硬土层侧向扩展、发生较大位移24。综上,考虑剪切局部化的数值模型能够较好地模拟倾斜液化场地不同土层的水平位移发展趋势。
图9给出了桩基最大曲率的数值模拟结果和模型试验结果的对比情况,可以看出两个结果沿着土体深度的变化趋势基本一致。桩基曲率在桩顶处的值最大,随后随着埋深的增加逐渐减小,在埋深为0.9 m处出现了转折并达到最小值;随着埋深的进一步增加而逐渐增大,在桩基底部达到了一个较大值。由于模型试验中桩基底部固定,而桩顶受上部结构惯性力影响,导致桩身曲率在桩顶和桩底处较大,本文的数值模拟也较好地模拟了这个变化趋势。
图10给出了上部结构的加速度时程曲线数值模拟结果和模型试验结果的对比情况,同样可以看出二者发展趋势基本一致。
通过上述对多个响应结果的对比验证可知,本文所建立的倾斜液化场地-群桩-结构相互作用二维整体化数值模型能够较好地模拟倾斜液化场地-桩基-结构振动台模型试验中土体和结构的动力响应规律,因此所采用的数值模拟方法是合理和有效的。
由于1g振动台试验尺寸规模较小以及模型箱效应的局限性,不能合理地反映实际场地土体的应力水平。因此本文基于已验证的方法建立典型倾斜液化场地-群桩-结构数值模型,以此来讨论上覆土层对实际倾斜液化场地-群桩-结构体系动力反应的影响。
选取某高铁渡河桥梁工程26,该桥为典型的钢筋混凝土连续梁桥。数值建模过程中将模型中场地土简化成两层,分别为黏土和砂土,其中饱和砂土相对密实度为55%;模型中土层总高度为20 m,长为100 m,地下水位位于饱和砂土层顶面。桩设计为2×2布置的高承台群桩,其中桩径为1.2 m,桩长为21 m,桩间距为4 m,桥墩高度为8 m,桥墩直径为2 m,承台采用混凝土材料,尺寸为7 m×7 m×3 m。基于上述数值建模的方法针对该实际场地在OpenSees中建立二维典型倾斜液化场地-群桩-结构数值模型。由于实际场地尺寸较大,简单的剪切边界条件已经不适用,因此在模型两侧各建立长为50 m,厚度为10000 m的自由场土体单元,并使用OpenSees中的equalDOF命令将自由场土体同一高度处的水平和竖向位移自由度进行约束,以此模拟实际场地的自由场边界条件。模型中其他的建模方法均与前述振动台试验建模方法一致。
本节以上述实际场地中距离上坡桩基28 m处的土体为研究对象,论文中后续分析均选取该位置来进行场地的土体响应的计算与讨论。上覆土层为不排水抗剪强度为75 kPa的黏土层。图11(a)给出了该位置处不同上覆土层厚度下饱和砂土沿深度方向的孔压比分布图。由图可知,在饱和砂土层中,土体的孔压比随着饱和砂土土层深度的增加而减小,由此说明浅层土体相比深层土体更易液化。同时可以看出,在土体较深的位置处,同一深度处土体的孔压比随着上覆土层厚度的增大均有所减小。当上覆土层厚度增加到5 m时,饱和砂土土体各土层孔压比均未达到1,也就是说饱和砂土层各个位置处的土体均未完全液化。图11(b)给出了不同上覆土层厚度下饱和砂土层顶面的土体的孔压比时程图,由图可以看出随着上覆土层厚度的增加,饱和砂土层达到液化的时刻也相应延迟,且土体的孔压比峰值也相应减小。以上充分说明了上覆土层厚度的增加有利于降低土体的液化程度。
图12给出了不同上覆土层厚度时各个土层的土体加速度峰值分布图。可以看出,不同情况下地震波加速度在土层中的传播趋势基本一致。沿着土体深度由下往上看,土体的加速度峰值在饱和砂土层中随着土体深度的减小出现明显衰减,在黏土层加速度出现增长,这与上述试验中观测到的规律一致。随着上覆土层厚度的增加,浅层土体处的加速度峰值出现明显的增大,尤其地表土体的加速度峰值增大了约0.9倍,这一现象与4.1节所计算得到的上覆土层厚度的增加使得土体的液化程度降低有关。
图13给出了不同上覆土层厚度时土体沿深度方向的水平残余位移分布图。可以看出,饱和砂土层的土体水平残余位移在深度15 m以下的部分增长幅度很小,在15 m以上土体水平残余位移出现明显增长;随着土体深度的减小,土体的水平残余位移不断增加,在饱和砂土层顶面处达到最大,而在黏土层的水平残余位移基本不变。随着上覆土层厚度的增加,相同深度处土体的水平残余位移均有所减小,上覆土层厚度从0增加到5 m时,土体的水平残余位移峰值从0.79 m减小至0.18 m,下降幅度约77%。因为上覆土层厚度的增加对场地土体的约束作用更加明显,土体的侧向变形减小更加显著。
图14给出了不同上覆土层厚度下桩基水平残余位移沿深度方向的分布图。可知,桩基水平残余位移在饱和砂土层埋深15 m以下的部分增长幅度很小,在15 m以上开始出现明显增长,并随着埋深的减小,桩基水平残余位移不断增加,这与土体的水平残余位移增长趋势基本一致;桩基水平残余位移到达黏土层时增长速度减慢,说明黏土层对桩基起到了一定的固定作用从而限制了桩基位移的发展。随着上覆土层厚度的增加,不同深度桩基的水平残余位移均有所减小,相比无上覆土层,上覆土层厚度增加至5 m,桩基水平残余位移峰值下降约68%。
图15给出不同上覆土层厚度时桩基曲率沿土层深度分布的包络图。由图15可知,不同计算工况下桩基曲率在土层深度12~13 m的范围内达到最大值,且由于惯性力的影响,桩基顶部的曲率也较大。当上覆土层的厚度超过1 m时,随着上覆土层厚度的增加,桩身的最大曲率及桩顶曲率出现明显的减小;当上覆土层厚度增加至5 m,桩顶最大曲率从0.01减小至0.002,下降约80%,桩身最大曲率从0.011减小至0.004,下降约64%。分析其原因,是因为上覆土层对桩基反应起到了约束作用,限制了桩基的运动,这与文献[527]的结论基本一致。因此,增加上覆土层厚度可以提高桩基的受力性能,可以作为一种减轻液化场地桩基震害的有效手段应用到实际工程中。
以上覆土层厚度为0和5 m为例,图16给出了埋深为13 m处土体在两种不同上覆土层厚度时对桩-土-结构相互作用影响的时程曲线图。
由图可知,针对无上覆土层来说,在地震作用前期(0~12 s)内,土体的液化程度较低,土体的水平残余位移增长缓慢,这时桩基曲率基本不变;在地震作用12 s,饱和砂土的孔压比ru达到0.8后,土体位移出现明显增长,桩基曲率也随之增长,且桩基曲率出现最大值的时刻与土体位移峰值时刻基本一致。由此可知,桩基曲率的变化主要受到土体位移变化的影响。相比无上覆土层的情况,有上覆土层存在时,土体的液化程度降低,土体的位移减小从而使得桩基曲率也减小。同时从桥墩曲率和上部结构加速度时程曲线可以看出,桥墩的曲率峰值出现时刻与上部结构加速度峰值出现时刻基本一致,桥墩曲率主要受上部结构惯性力的影响。相比无上覆土层,有上覆土层存在时,上覆土层使得上部结构的加速度增加,同时桥墩的曲率也有所增加。
为了更加全面地分析上覆土层对倾斜液化场地桩基地震响应的影响,针对不排水抗剪强度分别为18,37,75 kPa的上覆黏土层进行计算,结果如图17所示。图17(a)和(b)为上覆土层厚度为3 m时不同上覆土层性质下桩身水平残余位移分布图以及桩基曲率包络图。由图17(a),(b)可知,随着上覆黏土层强度的增加,同一深度处桩基的水平残余位移均有所减小,桩基出现最大曲率的位置发生改变,桩顶及桩身最大曲率均有所减小。图17(c)为不同上覆土层厚度时考虑上覆土层性质影响下的桩身最大残余水平位移、桩身最大曲率以及桩顶曲率的计算结果。由图17(c)可知,相同上覆土层厚度下,上覆土层的不排水抗剪强度越大,桩基位移、桩身曲率及桩顶曲率越小,尤其当上覆土层厚度大于2 m时,上覆土层强度对桩基动力反应的影响更加明显。
本文基于振动台模型试验,建立了倾斜液化场地桩-土-结构相互作用的整体有限元数值模型,验证了数值模拟方法的合理性和有效性。在此基础上,建立了针对实际场地的典型倾斜液化场地-群桩-结构数值模型,讨论了不同上覆土层厚度及性质对倾斜液化场地-桩基-上部结构体系地震动力反应的影响。得到的主要结论如下:
(1)本文考虑桩土接触非线性以及土体剪切局部化所建立的数值模型可以较好地模拟桩-土相互作用以及黏土层与饱和砂土层间交界处的响应。
(2)上覆土层厚度的增加使得饱和砂土层中的孔压比减小,浅层土体的加速度峰值增加,土体的水平残余位移减小。增加上覆土层厚度可以降低土层的液化程度和变形。
(3)随着上覆土层厚度增加,桩身位移以及桩基曲率均有所减小。上覆土层的存在可以提高桩基的受力性能。
(4)上覆土层的强度越大,桩基位移和桩身曲率越小。随着上覆土层厚度增加,上覆土层强度对桩基动力反应的影响更加明显。
  • 国家自然科学基金资助项目(52078016)
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ZHENG GZHANG W BZHOU H Z. Effects of nonliquefiable crust on the seismic behavior of pile foundations in liquefiable soils[C]//Conference on Performance-based Design in Earthquake. Geotechnical Engineering. Cham: Springer, 2022: 1265-1276.
2024年第37卷第12期
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doi: 10.16385/j.cnki.issn.1004-4523.2024.12.007
  • 接收时间:2022-11-18
  • 首发时间:2026-02-12
  • 出版时间:2024-12-28
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  • 收稿日期:2022-11-18
  • 修回日期:2023-02-24
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国家自然科学基金资助项目(52078016)
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    1北京工业大学建筑工程学院,北京 100124
    2北京工业大学城市与工程安全减灾教育部重点实验室,北京 100124
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2种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

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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