循环荷载作用下不均质地层中盾构隧道纵向响应研究
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摘要
修建在纵向不均质地层中的地铁隧道,由于列车循环荷载的作用,会导致隧道下部的土体产生不均匀沉降,对既有隧道产生不利的影响。针对这一问题,提出考虑隧道剪切效应的地基不均匀沉降对既有隧道竖向变形影响的解析解。既有隧道简化为搁置在Winkler地基上的Timoshenko梁,通过两阶段分析法,分析下卧地层不均匀沉降引起的隧道响应。首先确定列车荷载引起的动偏应力,并运用土层的力学指标计算出静偏应力和破坏偏应力。然后运用累积应变的经验公式计算出隧道下部土体的累计沉降,将土体的沉降转化为力施加在隧道上。基于Timoshenko梁理论,建立考虑隧道剪切效应的隧道竖向变形微分方程,求解得到隧道变形的解析解,进一步可以得到隧道的弯矩、剪力、转角、错台。
Subway tunnels built in longitudinal inhomogeneous formations will inevitably cause the differential settlement of the underlying soil because of the cyclic loading of trains. Differential soil settlement, in turn, adversely affects the safety of existing tunnels. An analytical solution for the effect of differential foundation settlement on the vertical deformation of existing tunnels and that considers the tunnel shear effect was proposed. The existing tunnel was assumed as a Timoshenko beam resting on a Winkler foundation. The two-stage approach was used to analyze the tunnel response caused by differential soil settlement. First, the dynamic deviator stress caused by the cyclic loading of trains was determined, and static deviator stress and failure deviator stress were calculated by using soil mechanical indexes. Second, the cumulative settlement of the soil underlying the tunnel was calculated by using the empirical equation of cumulative plastic strain and then transformed into the force imposed on the underlying shield tunnel. Finally, the differential equations for tunnel vertical deformation accounting for the shear effect of tunnel were established on the basis of Timoshenko beam theory. Then, the analytical solution was obtained through calculation, and the tunnel internal forces, including tunnel bending moment, shear force, rotation angle, and dislocation between adjacent rings, were further obtained in accordance with the proposed analytical method.
Subway tunnels built in longitudinal inhomogeneous formations will inevitably cause the differential settlement of the underlying soil because of the cyclic loading of trains. Differential soil settlement, in turn, adversely affects the safety of existing tunnels. An analytical solution for the effect of differential foundation settlement on the vertical deformation of existing tunnels and that considers the tunnel shear effect was proposed. The existing tunnel was assumed as a Timoshenko beam resting on a Winkler foundation. The two-stage approach was used to analyze the tunnel response caused by differential soil settlement. First, the dynamic deviator stress caused by the cyclic loading of trains was determined, and static deviator stress and failure deviator stress were calculated by using soil mechanical indexes. Second, the cumulative settlement of the soil underlying the tunnel was calculated by using the empirical equation of cumulative plastic strain and then transformed into the force imposed on the underlying shield tunnel. Finally, the differential equations for tunnel vertical deformation accounting for the shear effect of tunnel were established on the basis of Timoshenko beam theory. Then, the analytical solution was obtained through calculation, and the tunnel internal forces, including tunnel bending moment, shear force, rotation angle, and dislocation between adjacent rings, were further obtained in accordance with the proposed analytical method.
引文
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[21] ZHANG Z G,HUANG M S,WANG W D.Evaluation of Deformation Response for Adjacent Tunnels Due to Soil Unloading in Excavation Engineering[J].Tunnelling and Underground Space Technology,2013,38:244-253.
[22] ATTEWELL P B,YEATES J,SELBY A R.Soil Movements Induced by Tunnelling and Their Effects on Pipelines and Structures[M].Glasgow:Blackie and Son Ltd.,1986:10-50.
[2] 冷建,叶冠林,刘学增,等.循环荷载对上海软土动力特性影响规律的试验研究[J].地震工程学报,2015(4):1049-1052.LENG Jian,YE Guanlin,LIU Xuezeng,et al.Experimental Study On the Dynamic Characteristics of Shanghai Soft Clay Subjected to Cyclic Loading[J].China Earthquake Engineering Journal,2015(4):1049-1052.
[3] 李进军,黄茂松,王育德.交通荷载作用下软土地基累积塑性变形分析[J].中国公路学报,2006,19(1):1-5.LI Jinjun,HUANG Maosong,WANG Yude.Analysis of Cumulative Plastic Deformation of Soft Clay Foundation under Traffic Loading[J].China Journal of Highway and Transport,2006,19(1):1-5.
[4] 魏星,黄茂松.交通荷载作用下公路软土地基长期沉降的计算[J].岩土力学,2009,30(11):3342-3346.WEI Xing,HUANG Maosong.A Simple Method to Predict Traffic-load-induced Permanent Settlement of Road on Soft Subsoil[J].Rock and Soil Mechanics,2009,30(11):3342-3346.
[5] 边学成,曾二贤,陈云敏.列车交通荷载作用下软土路基的长期沉降[J].岩土力学,2008,29(11):2990-2996.BIAN Xuecheng,ZENG Erxian,CHEN Yunmin.Long-term Settlements of Soft Soil Ground Induced by Train Traffic Loadings[J].Rock and Soil Mechanics,2008,29(11):2990-2996.
[6] 吕玺琳,方航,张甲峰.循环交通荷载下软土路基长期沉降理论解[J].岩土力学,2016(增刊1):435-440.Lü Xilin,FANG Hang,ZHANG Jiafeng.ATheoretical Solution for Long-term Settlement of Soft Subgrade Induced by Traffic Loading[J].Rock and Soil Mechanics,2016(s1):435-440.
[7] 高广运,徐大为,张先林,等.地铁循环荷载作用下上海软土路基的长期沉降计算[J].桂林理工大学学报,2012,32(3):370-374.GAO Guangyun,XU Dawei,ZHANG Xianlin,et al.Long-Term Settlement Calculation of Shanghai Metro Soft Soil Foundation under Cyclic Loading[J].Journal of Guilin University of Technology,2012,32(3):370-374.
[8] WU H N,CHAI J C,XU Y S,et al.Evaluation of Train-Load-Induced Settlement in Metro Tunnels[J].Proceedings of the ICE-Geotechnical Engineering,2015,168(5):396-406.
[9] HUANG H W,GONG W P,KHOSHNEVISAN S,et al.Simplified Procedure for Finite Element Analysis of the Longitudinal Performance of Shield Tunnels Considering Spatial Soil Variability in Longitudinal Direction[J].Computers and Geotechnics,2015,64:132-145.
[10] MONISMITH C L,OGAWA N,FREEME C R.Permanent Deformation Characteristics of Subsoil Due to Repeated Loading[J].Transportation Research Record,1975,537:1-17.
[11] LI D Q,SELIG E T.Cumulative Plastic Deformation for Fine-Grained Subgrade Soils[J].Journal of Geotechnical Engineering,1996,122(12):1006-1013.
[12] CHAI J C,MIURA N.Traffic-Load-Induced Permanent Deformation of Road on Soft Subsoil[J].Journal of Geotechnical and Geoenvironmental Engineering,2002,128(11):907-916.
[13] TIMOSHENKO S P.LXVI.on the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars[J].The London,Edinburgh,and Dublin Philosophical Magazine and Journal of Science,1921,41(245):744-746.
[14] WU H N,SHEN S L,LIAO S M,et al.Longitudinal Structural Modelling of Shield Tunnels Considering Shearing Dislocation between Segmental Rings[J].Tunnelling and Underground Space Technology,2015,50:317-323.
[15] MINDLIN R D.Force at a Point in the Interior of a Semi-Infinite Solid[J].Physics,1936,7(5):195-202.
[16] 沈珠江.基于有效固结应力理论的粘土土压力公式[J].岩土工程学报,2000,22(3):353-356.SHEN Zhujiang.EarthPressure of Clay based on Effective Consolidation Stress Theory[J].Chinese Journal of Geotechnical Engineering,2000,22(3):353-356.
[17] 志波,由紀夫,川島,一彦,大日方,尚巳,et al.シールドトンネルの耐震解析に用いる長手方向覆工剛性の評価法[J].土木学会論文集,1988.
[18] VESIC A B.Bending of Beams Resting on Isotropic Solid[J].Journal of the Engineering Mechanics Division,1961,87.
[19] 梁荣柱,林存刚,夏唐代,等.考虑隧道剪切效应的基坑开挖对邻近隧道纵向变形分析[J].岩石力学与工程学报,2017,36(1):223-233.LIANG Rongzhu,LIN Cungang,XIA Tangdai,et al.Analysis on the Longitudinal Deformation of Tunnels Due to Pit Excavation Considering the Tunnel Shearing Effect[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(1):223-233.
[20] 张治国,黄茂松,王卫东.邻近开挖对既有软土隧道的影响[J].岩土力学,2009,30(5):1373-1380.ZHANG Zhiguo,HUANG Maosong,WANG Wei-dong.Responses of Existing Tunnels Induced by Adjacent Excavation in Soft Soils[J].Rock and Soil Mechanics,2009,30(5):1373-1380.
[21] ZHANG Z G,HUANG M S,WANG W D.Evaluation of Deformation Response for Adjacent Tunnels Due to Soil Unloading in Excavation Engineering[J].Tunnelling and Underground Space Technology,2013,38:244-253.
[22] ATTEWELL P B,YEATES J,SELBY A R.Soil Movements Induced by Tunnelling and Their Effects on Pipelines and Structures[M].Glasgow:Blackie and Son Ltd.,1986:10-50.