地表交通荷载引起邻近浅埋隧道振动评价研究
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摘要
为研究地表交通荷载引起邻近浅埋隧道振动问题,建立地表移动荷载下三维弹性半空间中隧道振动分析模型。隧道衬砌模拟为中空圆柱体,隧道周围土体模拟为含有圆柱形空腔的黏弹性半空间。地表车辆荷载简化为4个均布矩形荷载,矩形荷载可以分解为关于隧道轴线正对称和反对称2种荷载分量。含有圆柱形孔洞的地基中位移场分解为下行平面波引起的位移场和外行圆柱波引起的位移场,通过波场转换可对地表和衬砌–土体接触处的边界条件进行描述,在频域中获得控制方程基本解,然后利用快速Fourier变换获得时域结果求得。地表车辆荷载下邻近隧道的振动响应可由正对称和反对称荷载工况下的结果叠加得到。计算结果表明:隧道两侧车辆荷载在隧道处引起径向动应力最大值分布在以竖向为中心的-45°～45°范围;增加隧道埋深或车辆距隧道的水平距离,可显著减小隧道的振动速度响应和应力响应;一定隧道埋深下,车辆荷载与浅埋隧道的水平距离达到最小安全距离时隧道振动可以满足相关振动规范的要求,且该安全距离跟车辆速度在研究范围内呈线性关系。
In order to study the vibration of shallow tunnels caused by adjacent surface traffic loads,a threedimensional vibration prediction model for shallowly-buried tunnels generated by a moving surface loading was established,where the lining is simulated as a circular cavity and the ground around the tunnel is modeled as a viscoelastic half-space with a circular cavity. The vehicle load is represented by four rectangular pressures,which can be decomposed into symmetric and antisymmetric components with respect to the tunnel axis. The displacement field of the ground with a circular cavity is decomposed into the displacement fields respectively caused by the down-going plane wave and the outgoing cylindrical wave. The boundary conditions of soil-tunnel interface and ground surface are described through the transformation of plane and cylindrical waves,and the governing equations obtained from the frequency domain can be solved based on the time domain calculated by quick Fourier transform. The vibration of the tunnel under the moving surface vehicle nearby can be obtained by superimposing the results in the symmetric and antisymmetric loading cases. The calculation results show that the maximum radial dynamic stress caused by the vehicle load is distributed between-45°and 45°around the vertical direction. Increasing the tunnel depth or the horizontal distance between the vehicle and the tunnel can significantly reduce the vibration velocity and stress response of the tunnel. Under a certain tunnel depth,the tunnel vibration can meet the requirement of specifications when the distance between the vehicle load and the shallow tunnel exceeds the minimum safety distance,and the safety distance has a linear relationship with the vehicle speed in the studied range.
In order to study the vibration of shallow tunnels caused by adjacent surface traffic loads,a threedimensional vibration prediction model for shallowly-buried tunnels generated by a moving surface loading was established,where the lining is simulated as a circular cavity and the ground around the tunnel is modeled as a viscoelastic half-space with a circular cavity. The vehicle load is represented by four rectangular pressures,which can be decomposed into symmetric and antisymmetric components with respect to the tunnel axis. The displacement field of the ground with a circular cavity is decomposed into the displacement fields respectively caused by the down-going plane wave and the outgoing cylindrical wave. The boundary conditions of soil-tunnel interface and ground surface are described through the transformation of plane and cylindrical waves,and the governing equations obtained from the frequency domain can be solved based on the time domain calculated by quick Fourier transform. The vibration of the tunnel under the moving surface vehicle nearby can be obtained by superimposing the results in the symmetric and antisymmetric loading cases. The calculation results show that the maximum radial dynamic stress caused by the vehicle load is distributed between-45°and 45°around the vertical direction. Increasing the tunnel depth or the horizontal distance between the vehicle and the tunnel can significantly reduce the vibration velocity and stress response of the tunnel. Under a certain tunnel depth,the tunnel vibration can meet the requirement of specifications when the distance between the vehicle load and the shallow tunnel exceeds the minimum safety distance,and the safety distance has a linear relationship with the vehicle speed in the studied range.
引文
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[17] CAI Y,SUN H,XU C. Steady state responses of poroelastic half-space soil medium to a moving rectangular load[J]. International Journal of Solids and Structures,2007,44(22/23):7 183–7 196.
[18]曹志刚，孙思，袁宗浩，等.地表移动荷载对既有地下隧洞动力影响解析研究[J].岩土工程学报，2018,40(12):2 262–2 273.(CAO Zhigang,SUN Si,YUAN Zhonghao,et al. Analytical investigation of dynamic impact of moving surface loads on underground tunnel[J].Chinese Journal of Geotechnical Engineering,2018,40(12):2 262–2 273.(in Chinese))
[19] YUAN Z,CAO Z,BOSTR?M A,et al. The influence of pore-fluid in the soil on ground vibrations from a tunnel embedded in a layered half-space[J]. Journal of Sound and Vibration,2018;419:227–248.
[20]杨桂通，张善元.弹性动力学[M].北京：中国铁道出版社，1988:72–75.(YANG Guitong,ZHANG Shanyuan. Elastic dynamics[M].Beijing:Chinese Railway Press,1988:72–75.(in Chinese))
[21] HUNG H H,YANG Y B. Elastic waves in visco-elastic half-space generated by various vehicle loads[J]. Soil Dynamic and Earthquake Engineering,2001,21(1):1–17.
[22] International Organization for Standardization. ISO 04866 Mechanical vibration and shock—vibration of fixed structures—guidelines for the measurement of vibrations and evaluation of their effects on structures[S]. Switzerland:IHS Markit,2010.
[2] HUNG H H,CHEN G H,YANG Y B. Effect of railway roughness on soil vibrations due to moving trains by 2.5D finite/infinite element approach[J]. Engineering Structures,2013,57:254–266.
[3] BIAN X C,JIN W F,JIANG H G. Ground-borne vibrations due to dynamic loadings from moving trains in subway tunnels[J]. Journal of Zhejiang University—Science A(Applied Physics and Engineering),2012,13(11):870–876.
[4] FRAN?OIS S,SCHEVENELS M,GALVíN P,et al. A 2.5D coupled FE-BE methodology for the dynamic interaction between longitudinally invariant structures and a layered half-space[J].Computer Methods in Applied Mechanics and Engineering,2010,199(23):1 536–1 548.
[5] CLOUTEAU D,ARNST M,AL-HUSSAINI T M,et al. Freefield vibrations due to dynamic loading on a tunnel embedded in a stratified medium[J]. Journal of Sound and Vibration,2006,283(1):173–199.
[6] CHEBLI H,OTHMAN R,CLOUTEAU D,et al. 3D periodic BE-FE model for various transportation structures interacting with soil[J].Computers and Geotechnics,2008,35(1):22–32.
[7]谢伟平，孙洪刚.地铁运行时引起的土的波动分析[J].岩石力学与工程学报，2003,22(7):1 180–1 184.(XIE Weiping,SUN Honggang.FEM analysis on wave propagation in soils induced by high speed train loads[J]. Chinese Journal of Rock Mechanics and Engineering,2003,22(7):1 180–1 184.(in Chinese))
[8]和振兴，翟婉明，罗震.地铁列车引起的地面振动[J].西南交通大学学报，2008,43(2):218–221.(HE Zhenxing,ZHAI Wanming,LUO Zhen. Ground vibration caused by moving metro trains[J].Journal of Southwest Jiaotong University,2008,43(2):218–221.(in Chinese))
[9]张波，李术才，张敦福，等.岩石介质中地铁列车运行引起的环境振动响应研究[J].岩石力学与工程学报，2011,34(增1):1 366–1 379.(ZHANG Bo,LI Shucai,ZHANG Dunfu,et al. Research on rock environments vibration response induced by metro trains in rock media[J]. Chinese Journal of Rock Mechanics and Engineering,2011,34(Supp.1):1 366–1 379.(in Chinese))
[10] METRIKINE A V,VROUWENVELDER A C W M. Surface ground vibration due to a moving train in a tunnel:two-dimension model[J].Journal of Sound and Vibration,2000,234(1):43–66.
[11] FORREST J A,HUNT H E M. A three-dimensional tunnel model for calculation of train-induced ground vibration[J]. Journal of Sound and Vibration,2006,294(4):678–705.
[12]曾晨，孙宏磊，蔡袁强，等.简谐荷载作用下饱和土体中圆形衬砌隧道三维动力响应分析[J].岩土力学，2014,35(4):1 147–1 156.(ZENG Chen,SUN Honglei,CAI Yuanqiang,et al. Analysis of three-dimensional dynamic response of a circular lining tunnel in saturated soil to harmonic loading[J]. Rock and Soil Mechanics,2014,35(4):1 147–1 156.(in Chinese))
[13] YUAN Z,BOSTR?M A,CAI Y,et al. Analytical solution for calculating vibrations from twin circular tunnels[J]. Soil Dynamics and Earthquake Engineering,2019,117:312–327.
[14] SNEDDON I N. The stress produced by a pulse of pressure moving along the surface of a semi-infinite solid[J]. Rendiconti Del Circolo Matematico Di Palermo,1952,1(1):57–62.
[15] EASON G. The stresses produced in a semi-infinite solid by a moving surface force[J]. International Journal of Engineering Science,1965,2(6):581–609.
[16]刘干斌，汪鹏程，姚海林，等.矩形运动荷载作用下软土地基的三维振动研究[J].岩土力学，2006,27(10):1 658–1 662.(LIU Ganbin,WANG Pencheng,YAO Hailin,et al. 3D ground vibration of a soft subgrade in the vicinity of a moving rectangular load[J]. Rock and Soil Mechanics,2006,27(10):1 658–1 662.(in Chinese))
[17] CAI Y,SUN H,XU C. Steady state responses of poroelastic half-space soil medium to a moving rectangular load[J]. International Journal of Solids and Structures,2007,44(22/23):7 183–7 196.
[18]曹志刚，孙思，袁宗浩，等.地表移动荷载对既有地下隧洞动力影响解析研究[J].岩土工程学报，2018,40(12):2 262–2 273.(CAO Zhigang,SUN Si,YUAN Zhonghao,et al. Analytical investigation of dynamic impact of moving surface loads on underground tunnel[J].Chinese Journal of Geotechnical Engineering,2018,40(12):2 262–2 273.(in Chinese))
[19] YUAN Z,CAO Z,BOSTR?M A,et al. The influence of pore-fluid in the soil on ground vibrations from a tunnel embedded in a layered half-space[J]. Journal of Sound and Vibration,2018;419:227–248.
[20]杨桂通，张善元.弹性动力学[M].北京：中国铁道出版社，1988:72–75.(YANG Guitong,ZHANG Shanyuan. Elastic dynamics[M].Beijing:Chinese Railway Press,1988:72–75.(in Chinese))
[21] HUNG H H,YANG Y B. Elastic waves in visco-elastic half-space generated by various vehicle loads[J]. Soil Dynamic and Earthquake Engineering,2001,21(1):1–17.
[22] International Organization for Standardization. ISO 04866 Mechanical vibration and shock—vibration of fixed structures—guidelines for the measurement of vibrations and evaluation of their effects on structures[S]. Switzerland:IHS Markit,2010.
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