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运营地铁盾构隧道基底沉降的影响因素分析

徐平, 杨益新, 朱志豪

徐平,杨益新,朱志豪. 运营地铁盾构隧道基底沉降的影响因素分析[J]. 水文地质工程地质,2024,51(4): 157-166. DOI: 10.16030/j.cnki.issn.1000-3665.202308007
引用本文: 徐平,杨益新,朱志豪. 运营地铁盾构隧道基底沉降的影响因素分析[J]. 水文地质工程地质,2024,51(4): 157-166. DOI: 10.16030/j.cnki.issn.1000-3665.202308007
XU Ping, YANG Yixin, ZHU Zhihao. Analysis on settlement factors of shield tunnel foundation for operating metro[J]. Hydrogeology & Engineering Geology, 2024, 51(4): 157-166. DOI: 10.16030/j.cnki.issn.1000-3665.202308007
Citation: XU Ping, YANG Yixin, ZHU Zhihao. Analysis on settlement factors of shield tunnel foundation for operating metro[J]. Hydrogeology & Engineering Geology, 2024, 51(4): 157-166. DOI: 10.16030/j.cnki.issn.1000-3665.202308007

运营地铁盾构隧道基底沉降的影响因素分析

基金项目: 国家自然科学基金项目(51278467);铁科院集团公司重大基金(2022YJ280);河南省科技攻关(242102240019)
详细信息
    作者简介:

    徐平(1977—),男,博士,教授,主要从事岩土动力学和盾构隧道方面研究。E-mail:plian127@163.com

  • 中图分类号: U231+.3

Analysis on settlement factors of shield tunnel foundation for operating metro

  • 摘要:

    隧道基底沉降不仅影响地铁列车的正常运行和乘客的舒适性,严重时会造成隧道结构病害,目前的研究主要集中在长期沉降预测和单因素影响分析,非常有必要开展隧道基底沉降的多影响因素分析。以郑州地铁1号线某盾构隧道区间为工程实例,构建三维有限元数值模型,采用人工激振力模拟地铁列车竖向荷载,提取数值模拟结果的动应力和静偏应力数据,引入循环荷载作用下累积塑性应变计算公式,采用分层总和法计算得到隧道基底沉降,研究了隧道周围土层性质、道床脱空深度和地铁列车运行速度等因素对隧道基底沉降的影响,研究结果表明:数值模拟的隧道基底沉降和发展规律与现场实测结果具有较高的吻合度,验证了有限元模拟的准确性;隧道基底沉降随着周围土层砂粒含量的提高而减小;道床脱空尺寸会加剧隧道和道床板中应力集中和振动放大现象,增大隧道下卧土层的动偏应力和基底沉降;提高车速会增大基底沉降的横向影响范围;采用正交试验法、极差分析法和方差分析法得到了隧道沉降对各因素的敏感性,从大到小依次为:土层性质、车速和道床脱空,其中,土层性质为高度显著水平、车速为显著水平。研究成果对运营地铁盾构隧道的变形监测、安全评估和加固处理具有一定的参考价值。

    Abstract:

    The metro tunnel settlement would directly affect the normal train operation and the comfort of passengers; severe uneven settlement can easily cause tunnel structural diseases. The relevant studies mainly focused on long-term settlement prediction and single factor impact analysis; it is necessary to analyze the multiple factors that influence the tunnel foundation settlement. A three-dimensional finite element numerical model of one shield tunnel section of Zhengzhou metro 1st line was constructed and the vertical load of metro train was simulated as artificial excitation force to extract the dynamic stress and static deviator stress data. Introducing the cumulative plastic strain calculation formula under cyclic load, the layered summation method was used to calculate the tunnel foundation settlement. The influences of factors, such as the properties of soil where the tunnel is buried, the depth of track bed void, and metro operation velocity, on the tunnel foundation settlement were further analyzed. The results show that the numerical simulated foundation settlement and development law are consistent with on-site measured results, which verifies the accuracy of finite element simulation. The tunnel foundation settlement decreases with the increase of sand content in the surrounding soil layer; the size of the track bed void would exacerbate the stress concentration and vibration amplification in the tunnel and track bed slab, and then increase the dynamic deviatoric stress of soil layer under the tunnel and foundation settlement. Increasing the metro train velocity would increase the lateral influence range of foundation settlement. The sensitivity of tunnel settlement to various factors is obtained with orthogonal experimental method, range analysis method, and variance analysis method. The descending order of sensitivity is soil layer properties, train velocity, and track bed void, in which, soil layer property has a highly significant level and vehicle speed a has significant level. This study can provide basic information for the deformation monitoring, safety assessment, and reinforcement treatment of operating metro tunnels.

  • 地铁具有高效快捷、不受道路拥堵影响、运营时间长、环保节能等优势,已经成为国内大型城市重要的交通工具。随着隧道运营年限的增加,受列车运行振动荷载、下卧土层不均匀性、隧道上方超载、隧道周边基坑开挖和降水、地下水位上升、隧道渗漏、区域性地面沉降等因素的影响,隧道基底会产生较大的沉降,直接影响地铁列车的正常运行和乘客的舒适性[1],严重的不均匀沉降易造成结构病害,如管片接缝张开与错台、开裂、衬砌渗漏水、轨面变形超限等[2],甚至会引发安全问题,如隧道坍塌、地面塌陷、地表脱空、管道破损及建(构)筑物沉降变形[34]。因此,开展地铁盾构隧道基底沉降的影响因素分析,可以为运营期常见病害治理提供重要依据[57]

    近年来,国内外学者主要通过现场实测、理论分析、数值模拟等方法对地铁隧道基底的沉降进行了预测分析:如,刘明等[8]采用拟静力有限元计算和经验拟合计算模型相结合的方法,预测了地铁荷载作用下饱和软黏土地基的长期沉降;杨兵明等[9]依据淤泥质黏土的室内动三轴试验结果,将数值模拟与修正的指数预测模型相结合并运用分层总和法,对宁波轨道交通1号线某区间盾构隧道的长期沉降进行预测;薛阔等[10]采用理论分析和数值模拟的研究手段,预测了昆明地铁3号线某运营隧道基底的长期累积沉降;Huang等[11]引入循环流动性模型来模拟饱和软黏土的力学行为,研究了列车运行荷载引起地铁隧道的长期沉降;石钰锋等[12]预测了地铁隧道基底风化软岩在列车荷载作用下的长期沉降;王国才等[13]通过三维有限元模拟对比分析了不同列车时速下土体和衬砌的动力响应,并使用经验公式预测了软土地基在长期循环列车荷载作用下的累积变形;张研沁等[14]采用机器学习方法,建立了基于先期区域地质信息及隧道沉降学习资料的盾构隧道长期沉降预测模型。

    众多学者对隧道沉降的影响因素进行了研究分析:Tan等[15]通过现场测试和数值模拟相结合的方法,研究了基坑开挖对邻近地铁站和运营双盾构隧道沉降的影响;张书丰等[16]通过构建的盾构隧道沉降计算公式及典型案例,解释了盾构隧道不均匀沉降是由不均匀分布的下卧软土与外部影响因素共同作用所造成,明确了地下水位的下降对盾构隧道沉降影响最为显著,外部基坑施工影响次之,地表堆载影响较少;史玉金等[17]以上海地铁4号线隧道段监测数据为基础,从长期变形特征进行探讨,分析了地铁隧道变形与其下部土层变形之间的关系;钱晓华等[18]以郑州地铁1号线一期工程为研究背景,对隧道周边土体孔隙水压力进行了现场实测,并研究了小半径曲线段隧道周边土体孔隙水压力变化引起的隧道沉降规律;彭红霞等[19]、马龙祥等[20]、刘羽航等[21]和王晓睿等[22]以人工激励函数模拟地铁列车荷载,通过三维数值模拟,研究了地铁列车引起盾构隧道的沉降规律。

    上述研究主要集中在地铁盾构隧道及地基的长期沉降预测和引起沉降的单因素分析,截至目前,并未见关于隧道基底沉降多影响因素敏感性的研究报导。本文以郑州地铁1号线某盾构隧道区间为工程实例,构建三维有限元数值模型,采用人工激振力模拟地铁列车竖向荷载,提取数值模拟结果的动应力和静偏应力数据,引入循环荷载作用下累积塑性应变计算公式,采用分层总和法计算得到隧道基底沉降,研究了隧道周围土层性质、道床脱空深度和地铁列车运行速度等因素对隧道基底沉降的影响,相关成果可为地铁隧道基底沉降预测和加固处理提供依据。

    Chai等[23]充分考虑交通荷载的振动特性和循环加载特性,并假定地基土层的累积塑性应变εp随着初始静偏应力增加而增大,提出了εp的经验公式:

    εp=aNb(qdqf)j(1+qsqf)k (1)

    式中:εp——累积塑性应变;

    N——循环加载次数;

    qd——动偏应力/kPa;

    qs——初始静偏应力/kPa;

    qf——静破坏偏应力/kPa;

    abjk——经验参数,由试验确定。

    式(1)可以较好地模拟粉土在循环荷载作用下的累积塑性变形,计算效率更高,充分考虑了长期循环荷载作用下的主要影响因素:动偏应力qd、初始静偏应力qs和破坏静偏应力qf

    黄凯[24]根据郑州地区粉土在不同静止土压力系数、围压和动荷载等条件下的循环荷载下累积塑性应变曲线,求得:a=4.8、b=0.2、j=1.7、k=1,代入式(1)可确定郑州粉土在循环荷载作用下的εp计算式:

    εp=4.8N0.2(qdqf)1.7(1+qsqf) (2)

    将地铁盾构隧道基底土体划分为n层,根据动力有限元等方法,由式(2)计算第i层土体的长期不排水累积变形εpi,通过分层总和法可得到隧道基底沉降S

    S=ni=1εpihi (3)

    式中:εpi——第i层土的累积塑性变形;

    hi——第i层土的厚度/m;

    n——划分的土体层数。

    郑州地铁1号线运营至今约10 a,某区间的盾构隧道出现了较大的沉降,最大基底沉降达到32.5 mm,已经影响地铁列车的正常运行和乘客的舒适性。该区间隧道的覆土厚度12~16 m,场地地层从上至下依次为杂填土、粉土、粉质黏土夹粉砂、细砂、粉质黏土,土层的相关参数见表1

    表  1  土层的相关参数
    Table  1.  Relevant parameters of soils
    土层 平均层厚
    /m
    密度
    /(g·cm−3
    弹性模量
    /MPa
    泊松比 黏聚力
    /kPa
    内摩擦角
    /(°)
    杂填土 2.3 1.80 25.0 0.33 10.1 19.2
    粉土 11.7 1.94 33.0 0.38 13.7 20.8
    粉质黏土夹粉砂 7.0 2.00 45.0 0.37 14.6 23.2
    细砂 10.2 2.13 62.4 0.35 0.0 30.0
    粉质黏土 14.4 1.98 37.0 0.31 26.8 19.3
    下载: 导出CSV 
    | 显示表格

    盾构隧道为C50钢筋混凝土管片结构,外径6.2 m、壁厚0.35 m,道床为现浇C35钢筋混凝土结构,厚0.38 m,隧道和道床相关参数见表2

    表  2  隧道和道床的相关参数
    Table  2.  Relevant parameters of tunnel and track bed
    隧道结构密度/(g·cm−3弹性模量/GPa泊松比
    隧道2.5034.50.20
    道床2.4531.50.20
    下载: 导出CSV 
    | 显示表格

    采用有限元软件ABAQUS构建道床-隧道-周围土体的三维模型,3个方向的尺寸分别为:Z方向(列车行进方向为正)100 m、Y方向(垂直向下为正)45 m、X方向(面向列车行进方向,水平向右为正)50 m,土体采用Mohr-Coulomb模型,隧道和道床采用弹性模型[2526],采用sweep划分技术和中性轴算法进行网格划分,对隧道周围1倍直径范围区域及脱空区域进行网格加密,有限元模型及网格划分如图1所示,共划分101000单元(其中,土体62192单元、衬砌11232单元、道床27576单元)。

    图  1  有限元模型及网格划分
    Figure  1.  Finite element model and mesh generation

    根据沉降监测和地质雷达无损检测等资料得知,影响地铁盾构隧道基底沉降的主要因素为:隧道周围土层性质、道床与隧道之间的脱空、地铁列车的行驶荷载,选取以下工况进行数值模拟分析。

    (1)土层性质

    由于隧道周围、基底以及下卧层的土体往往是不均匀的,而地铁列车运行产生的荷载幅值和频率也具有随机性,地铁列车振动引起隧道基底土层的扰动、沉降量和沉降时间等都有不同程度的差异,另外,即使同一种土体,在不同振幅和频率的振动荷载作用下产生的动力响应特性也会存在较大的差异。

    选取的郑州地铁1号线某区间的隧道平均覆土厚度14 m,隧道主要位于粉质黏土夹粉砂层中,由于地层的分布存在差异,隧道局部位于细砂和粉质黏土中,为了探究隧道周围土层性质对运营隧道基底沉降的影响,第三层土的厚度取7 m,土层类别分别取粉砂、粉质黏土夹粉砂和粉质黏土。

    (2)道床脱空

    经地质雷达无损检测探明,该区间的道床与隧道之间存在大面积脱空现象,脱空区域的最大尺寸为长4 m、宽2 m、深4 m,主要分布于双轨中间的正下方,在数值模拟时,选取3种不同程度的道床脱空尺寸:① 无脱空情况;② 脱空长4 m、宽2 m、深2 cm;③ 脱空长4 m、宽2 m、深4 cm。

    (3)地铁列车振动荷载

    潘昌实等[27]以人工激振力模拟列车竖向荷载,采用Newmark隐式时间积分法求解结构体系的二阶运动微分方程组,建立了激振力函数Ft)的表达式:

    F(t)=P0+P1sinω1t+P2sinω2t+P3sinω3t (4)
    Pi=M0aiω2i(i=1,2,3) (5)
    ωi=2πv/Li(i=1,2,3) (6)

    式中:F(t)——列车振动荷载/kN;

    P0——车轮静载/kN;

    Pi——不同控制条件下的振动荷载幅值/kN;

    ωi——不同控制条件下的振动圆频率/Hz;

    Li——不同控制条件下的振动波长/m;

    ai——不同控制条件下的矢高/mm;

    M0——簧下质量/kg;

    v——地铁列车运行速度/(km·h−1)。

    郑州地铁1号线采用A型车,全车6节编组,列车最高行驶速度为80 km/h,单节车的参数如下[28]:车长19 m、车宽2.8 m、轴距2.2 m、车辆轴重14 t、轮对质量1.42 t,轨距1.435 m。在式(4)—(6)中,取P0=70 kN、M0=750 kg,行车平顺性、动力附加荷载和波形磨耗3种控制条件下的振动波长Li和矢高ai分别取[29]L1=10 m、L2=5 m、L3=2 m、a1=0.6 mm、a2=0.5 mm、a3=0.1 mm,为了研究车速对隧道基底长期沉降的影响,选取3种车速:低速v=40 km/h、中速v=60 km/h和高速v=80 km/h。

    将隧道周围土层设置为粉质黏土夹粉砂,车速取80 km/h,道床脱空尺寸设置为长4 m、宽2 m、深2 cm,通过在道床底部设置单元缺失来模拟道床脱空的情况,根据数值模拟的动力响应结果提取动偏应力和静偏应力,由式(2)求得每层土体的竖向变形,通过分层总和法计算得到了隧道轴线正下方隧道基底的累积沉降,数值模拟与现场实测的基底沉降随运营时间的变化曲线,如图2所示。

    图  2  数值模拟与现场实测隧道基底沉降曲线
    Figure  2.  Numerical simulated and on-site measured settlement curves of tunnel foundation

    图2可以看出,数值模拟的隧道基底沉降和发展规律与现场实测结果具有较高的吻合度,地铁运营至第7年时,基底沉降曲线趋于平缓,沉降已基本完成,数值模拟和现场实测的基底沉降值分别为29.41 mm和31.51 mm,两者相差6.71%,说明有限元模型是合理的,可以开展沉降影响因素的研究分析。

    不考虑道床脱空,车速取80 km/h,隧道周围土层分别设置为粉砂、粉质黏土夹粉砂和粉质黏土。

    地铁列车运行引起隧道基底(含下卧土层)的位移、速度和加速度峰值沿深度的分布曲线,如图3所示。

    图  3  隧道周围土层对基底位移、速度和加速度峰值的影响
    Figure  3.  Influences of tunnel surrounding soils on the displacement, velocity, and peak acceleration of surrounding foundation

    图3可以看出,地铁列车运行荷载在粉质黏土中产生的振动影响较大,沿深度方向衰减也最为迅速,主要是因为地铁列车行驶过程中产生的动轮压通过钢轨传递给道床和隧道,隧道作为二次振源进一步引起周围土体的振动,粉质黏土的黏聚力和阻尼相对较大,波能耗散较快,因此地铁列车的振动极易在粉质黏土中产生较大的塑性变形积累,最终引起基底的沉降变形。

    隧道处于不同土层情况下,隧道基底累积沉降随运营时间的变化曲线,如图4所示。

    图  4  不同隧道周围土层的基底沉降曲线
    Figure  4.  Cumulative settlement curves of foundation under different surrounding soils

    图4可以看出,隧道周围土层性质对隧道基底沉降的影响很大,地铁运营至第7年时,粉质黏土、粉质黏土夹粉砂和粉砂3种情况下的最大沉降分别为35.08,27.50,23.09 mm,隧道处于粉质黏土时比粉砂增加11.99 mm,增幅51.94%。3类土体的强度从强到弱依次为粉砂、粉质黏土夹粉砂、粉质黏土,土体越软,地铁列车振动引起的扰动和塑性变形越大,基底沉降也越大,而土体越硬,则地铁振动波可以快速传递到深层土体,一般来讲,土体的强度随着砂粒含量的增多而提高,因而粉砂的基底沉降相对较小,因此,通过注浆加固等施工工艺提高隧道周围土体的强度,可以减小运营期间隧道的基底沉降。

    将隧道周围土层设置为粉质黏土夹粉砂,车速取80 km/h行驶,考虑3种道床脱空情况,绘制了隧道基底的位移、速度和加速度峰值沿深度的分布曲线,如图5所示。

    图  5  道床脱空尺寸对基底位移、速度和加速度峰值的影响
    Figure  5.  Influences of track bed void size on the displacement, velocity, and peak acceleration of the foundation

    图5可以看出,随着道床脱空深度的增加,隧道基底的位移、速度和加速度峰值均随之增大,对于隧道基底下卧层深处的土体,位移、速度和加速度的时程峰值逐渐趋于相等,即道床脱空主要影响隧道-土体界面处的土体位移、速度和加速度。

    不同道床脱空尺寸情况下,隧道基底累积沉降随运营时间的变化曲线,如图6所示。

    图  6  不同道床脱空尺寸的隧道基底沉降曲线
    Figure  6.  Cumulative settlement curves of foundation under different track bed void sizes

    图6可以看出,随着道床脱空深度的增加,隧道基底沉降有所增大,地铁运营至第7年时,无脱空、脱空深2 cm和脱空深4 cm 3种情况下的基底沉降依次为27.50,29.41,30.53 mm,脱空深4 cm时隧道基底的沉降比无脱空增加3.02 mm,增幅10.99%。当道床与隧道之间存在脱空时,列车运行产生的振动通过钢轨传递给道床和隧道,会在隧道产生振动放大现象,从而增大隧道基底及下卧土层的动偏应力和塑性变形。

    不考虑道床的脱空,将隧道周围土层设置为粉质黏土夹粉砂,车速分别取40,60,80 km/h。当车速改变时,列车产生的振动荷载也会随之发生改变,从而在土层中产生不同的动力响应。

    不同车速情况下,隧道基底(含下卧土层)的位移、速度和加速度峰值沿深度的分布曲线,如图7所示。

    图  7  车速对基底位移、速度和加速度峰值的影响
    Figure  7.  Influences of train velocity on the displacement, velocity, and peak acceleration of the foundation

    图7可以看出,当地铁列车以低速40 km/h运行时,隧道基底位移、速度和加速度比较大,而当地铁列车以高速80 km/h运行时,土层中位移、速度和加速度峰值最小;随着深度的增加,基底位移和加速度峰值逐渐趋于稳定。

    不同车速情况下,隧道基底沉降变形随运营时间的变化曲线,如图8所示。

    图  8  不同车速的基底沉降曲线
    Figure  8.  Cumulative settlement curves of foundation under different train velocities

    图8可以看出,随着车速的提高,基底累积沉降变形逐渐减小,地铁运营至第7年时,车速在40,60,80 km/h 3种情况下的最大沉降值分别为33.01,30.55,27.50 mm,由于道床和隧道的刚度远大于基底及下卧层土体,而列车和乘客的总荷载基本保持不变,当车速下降时,延长了列车在同一位置停驻的时间,使土体产生较大的压缩变形,在地铁运营时间和列车运行次数相同的情况下,久而久之表现为地铁列车低速运行会增大隧道基底沉降。

    不同车速情况下,隧道轴线中心位置截面处(Z=50 m)的隧道基底沉降沿垂直于隧道轴线的横向变化曲线(即基底的沉降槽),如图9所示。

    图  9  不同车速的基底沉降槽曲线
    Figure  9.  Foundation settlement troughs under different train velocities

    图9可以看出,隧道沉降槽曲线为左右对称图形,与Peck沉降曲线基本一致[30],当地铁列车以不同速度运行时,基底最大沉降和沉降槽宽度均存在一定的差异,随着车速的提高,隧道基底最大沉降有所降低,但隧道轴线横截面的沉降槽宽度则明显增大,车速40,60,80 km/h对应的沉降槽宽度分别为44,36,30 m,提高车速会增大基底沉降的横向影响范围。

    采用正交试验法[3132]设计影响地铁隧道基底沉降的各因素和水平的组合,采用3因素3水平、无空列正交设计表,共有9种模拟试验方案,正交试验因素和水平见表3

    表  3  正交试验因素与水平
    Table  3.  Orthogonal experimental factors and levels
    因素土层性质脱空深度/cm车速/(km·h−1
    水平1A040
    水平2B260
    水平3C480
      注:表中A为粉质黏土,B为粉质黏土夹粉砂,C为粉砂。
    下载: 导出CSV 
    | 显示表格

    以隧道基底沉降为正交试验指标,通过数值模拟得到了正交试验结果,见表4。极差分析计算结果见表5

    表  4  正交试验结果汇总
    Table  4.  Summary of orthogonal test results
    组合 土层性质 脱空深度/cm 车速/(km·h−1 沉降/mm
    1 A 0 40 38.92
    2 A 2 60 37.73
    3 A 4 80 36.48
    4 B 0 60 30.55
    5 B 2 80 29.41
    6 B 4 40 34.51
    7 C 0 80 23.09
    8 C 2 40 27.29
    9 C 4 60 26.14
    下载: 导出CSV 
    | 显示表格
    表  5  正交试验结果直观分析
    Table  5.  Visual analysis of orthogonal test
    响应值 土层性质 脱空深度 车速
    K1 37.71 30.85 33.57
    K2 31.49 31.48 31.47
    K3 25.51 32.38 29.66
    R 12.20 1.52 3.88
    下载: 导出CSV 
    | 显示表格

    K1K2K3分别代表了土层性质(粉质黏土、粉质黏土夹粉砂和粉砂)、脱空深度(无脱空、脱空深2 cm和脱空深4 m)和车速(40,60,80 km/h)在3种水平下产生的基底沉降值,可以体现3个因素不同水平对基底沉降的影响,根据K1K2K3的数值可以分析得出:①隧道周围土层对基底沉降的响应值由大到小依次为粉质黏土、粉质黏土夹粉砂和粉砂,即隧道周围地层越软,基底沉降越大;②道床的脱空深度响应值,对隧道基底沉降的响应值由大到小依次为脱空深4 cm、脱空深2 cm和无脱空,道床脱空造成了列车运行产生的振动的放大现象,隧道基底及下卧土体中的动偏应力增大,从而导致土体塑性变形增大;③车速对隧道基底沉降的响应值由大到小依次为40,60,80 km/h,道床和隧道的刚度远大于基底及下卧层土体,而列车和乘客的总荷载基本保持不变,车速降低时,列车通过同一位置的时间延长,在荷载持续作用下,作用效应(沉降变形)却有所增强,隧道基底沉降会有所增大,而提高车速会增大基底沉降的横向影响范围。R表示某因素在各水平下基底沉降的极差,反映的该因素对隧道长期沉降量影响程度的大小,R值越大,代表该因素在隧道变形影响因素中权重越大,反之,权重越小,为次要因素。根据R值可知,各因素对隧道基底的影响由大到小依次为土层性质、车速和道床脱空深度。

    针对不同置信水平,正交试验的方差计算结果见表6

    表  6  正交试验方差分析
    Table  6.  Analysis of variance in orthogonal experiments
    因素偏差平方和自由度FF临界值
    0.900.950.99
    土层性质223.4121 128.2191999
    脱空深度3.5223.5691999
    车速23.01222.8891999
    误差0.192
      注:F为检验统计量,与给定的F临界值比较,做出决策。
    下载: 导出CSV 
    | 显示表格

    表6可知,对于不同试验因素下的长期沉降值而言,土层性质为高度显著水平(F>99),车速为显著水平(F>19),脱空深度的F虽然小于9,未达到显著水平,但脱空深度的偏差平方和3.52远大于误差的偏差平方和0.19,则可判定该试验中误差影响相对较小,正交试验结果合理性满足要求。

    (1)以郑州地铁1号某盾构隧道区间为工程实例,构建了三维有限元模型,数值模拟的隧道基底沉降和发展规律与现场实测结果具有较高的吻合度,地铁运营至第7年时,基底沉降曲线趋于平缓,沉降已基本完成,数值模拟和现场实测的基底沉降值分别为29.41,31.51 mm,两者相差6.71%,验证了有限元模拟的合理性和准确性。

    (2)隧道周围土层对基底沉降的响应值由大到小依次为粉质黏土、粉质黏土夹粉砂和粉砂,土体越软,地铁列车振动引起的扰动和塑性变形越大,基底沉降越大,而随着砂粒含量的提高,基底沉降呈减小的趋势。

    (3)随着道床脱空深度的增大,隧道基底沉降呈增大趋势,道床与隧道存在脱空时,列车运行产生的振动会出现放大现象,隧道基底及下卧土体中的动偏应力增大,从而导致土体塑性变形增大。

    (4)随着车速的提高,基底沉降有所减小,道床和隧道的刚度远大于基底及下卧层土体,而列车和乘客的总荷载基本保持不变,车速降低时,列车通过同一位置的时间延长,在荷载的持续作用下,作用效应(沉降变形)却有所增强,基底沉降反而会提高,但提高车速,基底沉降槽的宽度有所增加,车速越快,对基底沉降的横向影响范围越广。

    (5)采用正交试验法设计影响地铁隧道基底沉降的各因素和水平的组合,结合极差分析法和方差分析法,得出隧道基底沉降对各因素敏感性从大到小依次为土层性质、车速和道床脱空,其中土层性质为高度显著水平、车速为显著水平,在对敏感性大小排序的同时,排除了试验误差的可能,验证了模拟结果的合理性。

  • 图  1   有限元模型及网格划分

    Figure  1.   Finite element model and mesh generation

    图  2   数值模拟与现场实测隧道基底沉降曲线

    Figure  2.   Numerical simulated and on-site measured settlement curves of tunnel foundation

    图  3   隧道周围土层对基底位移、速度和加速度峰值的影响

    Figure  3.   Influences of tunnel surrounding soils on the displacement, velocity, and peak acceleration of surrounding foundation

    图  4   不同隧道周围土层的基底沉降曲线

    Figure  4.   Cumulative settlement curves of foundation under different surrounding soils

    图  5   道床脱空尺寸对基底位移、速度和加速度峰值的影响

    Figure  5.   Influences of track bed void size on the displacement, velocity, and peak acceleration of the foundation

    图  6   不同道床脱空尺寸的隧道基底沉降曲线

    Figure  6.   Cumulative settlement curves of foundation under different track bed void sizes

    图  7   车速对基底位移、速度和加速度峰值的影响

    Figure  7.   Influences of train velocity on the displacement, velocity, and peak acceleration of the foundation

    图  8   不同车速的基底沉降曲线

    Figure  8.   Cumulative settlement curves of foundation under different train velocities

    图  9   不同车速的基底沉降槽曲线

    Figure  9.   Foundation settlement troughs under different train velocities

    表  1   土层的相关参数

    Table  1   Relevant parameters of soils

    土层 平均层厚
    /m
    密度
    /(g·cm−3
    弹性模量
    /MPa
    泊松比 黏聚力
    /kPa
    内摩擦角
    /(°)
    杂填土 2.3 1.80 25.0 0.33 10.1 19.2
    粉土 11.7 1.94 33.0 0.38 13.7 20.8
    粉质黏土夹粉砂 7.0 2.00 45.0 0.37 14.6 23.2
    细砂 10.2 2.13 62.4 0.35 0.0 30.0
    粉质黏土 14.4 1.98 37.0 0.31 26.8 19.3
    下载: 导出CSV

    表  2   隧道和道床的相关参数

    Table  2   Relevant parameters of tunnel and track bed

    隧道结构密度/(g·cm−3弹性模量/GPa泊松比
    隧道2.5034.50.20
    道床2.4531.50.20
    下载: 导出CSV

    表  3   正交试验因素与水平

    Table  3   Orthogonal experimental factors and levels

    因素土层性质脱空深度/cm车速/(km·h−1
    水平1A040
    水平2B260
    水平3C480
      注:表中A为粉质黏土,B为粉质黏土夹粉砂,C为粉砂。
    下载: 导出CSV

    表  4   正交试验结果汇总

    Table  4   Summary of orthogonal test results

    组合 土层性质 脱空深度/cm 车速/(km·h−1 沉降/mm
    1 A 0 40 38.92
    2 A 2 60 37.73
    3 A 4 80 36.48
    4 B 0 60 30.55
    5 B 2 80 29.41
    6 B 4 40 34.51
    7 C 0 80 23.09
    8 C 2 40 27.29
    9 C 4 60 26.14
    下载: 导出CSV

    表  5   正交试验结果直观分析

    Table  5   Visual analysis of orthogonal test

    响应值 土层性质 脱空深度 车速
    K1 37.71 30.85 33.57
    K2 31.49 31.48 31.47
    K3 25.51 32.38 29.66
    R 12.20 1.52 3.88
    下载: 导出CSV

    表  6   正交试验方差分析

    Table  6   Analysis of variance in orthogonal experiments

    因素偏差平方和自由度FF临界值
    0.900.950.99
    土层性质223.4121 128.2191999
    脱空深度3.5223.5691999
    车速23.01222.8891999
    误差0.192
      注:F为检验统计量,与给定的F临界值比较,做出决策。
    下载: 导出CSV
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  • 收稿日期:  2023-08-06
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