双线隧道不同布置方式下相互作用影响的地层位移解析
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摘要
双线隧道开挖引起地层变形的既有理论研究,一般基于单线隧道计算结果直接采用线性叠加进行分析,而忽略了双线隧道之间的相互作用影响。为研究近距离地下工程开挖的相互影响,基于位移控制Schwarz交替法和复变函数理论,结合隧道洞周椭圆化收敛变形边界条件,提出了任意布置方式下双线盾构隧道开挖引起周围地层变形的计算方法。该方法以位移控制边界条件进行求解,体现了双线隧道开挖间的相互作用影响。通过离心试验和工程实例,将基于位移控制Schwarz交替法的复变函数理论解与线性叠加法解答以及实测数据进行了对比验证;针对双线隧道水平和斜交两种不同布置方式进行相关参数分析,获取了双线隧道间距变化引起的地层变形影响规律。结果表明:基于位移控制Schwarz交替法的复变函数方法求解得到的地表沉降曲线与实测值吻合较好,而直接线性叠加法解答存在较大误差。在地层等值线图规律分析中,水平与斜交布置下,两个隧道周围土体等值线图产生较为明显的相互"吸引"现象,隧道上方的土体沉降峰值线均向双线隧道中间倾斜,但随着双线隧道间距增加,"吸引"现象逐渐减弱。研究成果对于近距离双线盾构隧道开挖施工的现场保护措施制定提供一定的理论依据。
The existing theoretical researches on deformation of soils caused by twin-tunnel excavation are generally based on the linear superposition of single tunneling results and seldom consider the interaction effects between the two tunnels.Based on the displacement-controlled Schwarz alternating method and the complex variable function theory,and considering the oval deformation contraction boundary condition of tunnel opening,a method is proposed to analyze the deformation of the surrounding soils caused by twin-shield tunnel excavation in arbitrary position in order to reveal the interaction influences for the closed underground excavation.The method is based on the displacement boundary condition,which reflects the interaction between the twin tunnels during excavation.Through experiments and engineering cases,the theoretical solutions to the complex variable function based on the displacement-controlled Schwarz alternating method are obtained and compared with those of the linear superposition method and the measured data.The deformation influence laws of ground,which are caused by the variation of space between twin tunnels under two different layout patterns,horizontal and oblique,are acquired through parameter analyses.The results indicate that the surface settlement curve obtained by the complex variable function method based on the displacement-controlled Schwarz alternating method is in good agreements with the measured one,while the linear superposition method has a comparatively large error.Analysis of the laws of contour map indicates that in parallel and oblique positions,the contours of the soil around the twins tunnel produce the obvious "attracting" phenomenon,and the settlement peak line above the tunnels is inclined to the centre of the twin tunnels,but with the increase of the spacing between the twin tunnels,the phenomenon of "attracting" is gradually weakened.The research results may provide some theoretical basis for the protection measures of twin-shield tunnel excavation.
The existing theoretical researches on deformation of soils caused by twin-tunnel excavation are generally based on the linear superposition of single tunneling results and seldom consider the interaction effects between the two tunnels.Based on the displacement-controlled Schwarz alternating method and the complex variable function theory,and considering the oval deformation contraction boundary condition of tunnel opening,a method is proposed to analyze the deformation of the surrounding soils caused by twin-shield tunnel excavation in arbitrary position in order to reveal the interaction influences for the closed underground excavation.The method is based on the displacement boundary condition,which reflects the interaction between the twin tunnels during excavation.Through experiments and engineering cases,the theoretical solutions to the complex variable function based on the displacement-controlled Schwarz alternating method are obtained and compared with those of the linear superposition method and the measured data.The deformation influence laws of ground,which are caused by the variation of space between twin tunnels under two different layout patterns,horizontal and oblique,are acquired through parameter analyses.The results indicate that the surface settlement curve obtained by the complex variable function method based on the displacement-controlled Schwarz alternating method is in good agreements with the measured one,while the linear superposition method has a comparatively large error.Analysis of the laws of contour map indicates that in parallel and oblique positions,the contours of the soil around the twins tunnel produce the obvious "attracting" phenomenon,and the settlement peak line above the tunnels is inclined to the centre of the twin tunnels,but with the increase of the spacing between the twin tunnels,the phenomenon of "attracting" is gradually weakened.The research results may provide some theoretical basis for the protection measures of twin-shield tunnel excavation.
引文
[1]ELWOOD D E Y,MARTIN C D.Ground response of closely spaced twin tunnels constructed in heavily overconsolidated soils[J].Tunnelling and Underground Space Technology,2016,51(1):226-237.
[2]夏元友,陈春舒,BAKRI M,等.浅埋隧道开挖引起的土体水平位移分析[J].岩土力学,2015,36(2):354-360.(XIAYuan-you,CHEN Chun-su,BAKRI M,et al.Analysis of horizontal displacement of soil induced by shallow tunnel excavation[J].Rock and Soil Mechanics,2015,36(2):354-360.(in Chinese))
[3]楼晓明,郑俊杰,章荣军.隧道施工引起的地表变形数值模拟[J].铁道工程学报,2007,108(9):62-66.(LOUXiao-ming,ZHENG Jun-jie,ZHANG Rong-jun.Simulation of numerical values of surface deformation caused by tunnel construction[J].Journal of Railway Engineering Society,2007,108(9):62-66.(in Chinese))
[4]郑刚,张扶正,张天奇,等.盾构隧道开挖及补偿注浆对地层扰动影响的室内试验及数值模拟研究[J].岩土工程学报,2016,38(10):1741-1753.(ZHENG Gang,ZHANGFu-zheng,ZHANG Tian-qi,et al.Disturbance of shield tunnel excavation and compensation grouting to surrounding soil:laboratory tests and numerical simulations[J].Chinese Journal of Geotechnical Engineering,2016,38(10):1741-1753.(in Chinese))
[5]陈仁朋,齐立志,汤旅军,等.砂土地层盾构隧道开挖面被动破坏极限支护力研究[J].岩石力学与工程学报,2013,31(增刊1):2877-2882.(CHEN Ren-peng,QI Li-zhi,TANG Lü-jun,et al.Study of limit supporting force of excavation face's passive failure of shield tunnels in sand strata[J].Chinese Journal of Rock Mechanics and Engineering,2013,31(S1):2877-2882.(in Chinese))
[6]王俊,何川,胡瑞青,等.土压平衡盾构掘进对上软下硬地层扰动研究[J].岩石力学与工程学报,2017,36(4):953-963.(WANG Jun,HE Chuan,HU Rui-qing,et al.Soil disturbance induced by EPB shield tunnelling in upper-soft and lower-hard ground[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(4):953-963.(in Chinese))
[7]叶飞,苟长飞,陈治,等.盾构隧道同步注浆引起的地表变形分析[J].岩土工程学报,2014,36(4):618-624.(YEFei,GOU Chang-fei,CHEN Zhi,et al.Ground surface deformation caused by synchronous grouting of shield tunnels[J].Chinese Journal of Geotechnical Engineering,2014,36(4):618-624.(in Chinese))
[8]MO P Q,YU H S.Undrained cavity-contraction analysis for prediction of soil behavior around tunnels[J].International Journal of Geomechanics,2017,17(5):04016121.
[9]VERRUIJT A.A complex variable solution for a deforming circular tunnel in an elastic half-plane[J].International Journal for Numerical and Analytical Methods in Geomechanics,1997,21(21):77-89.
[10]韩凯航,张成平,王梦恕.浅埋隧道围岩应力及位移的显式解析解[J].岩土工程学报,2014,36(12):2253-2259.(HAN Kai-hang,ZHANG Cheng-ping,WANG Meng-shu.Explicit analytical solutions for stress and displacement of surrounding rock in shallow tunnels[J].Chinese Journal of Geotechnical Engineering,2014,36(12):2253-2259.(in Chinese))
[11]PARK K H.Elastic solution for tunneling-induced ground movements in clays[J].International Journal of Geomechanics,2004,4(4):310-318.
[12]BOBET A.Drained and undrained response of deep tunnels subjected to far-field shear loading[J].Tunnelling and Underground Space Technology,2010,25(1):21-31.
[13]唐晓武,朱季,刘维,等.盾构施工过程中的土体变形研究[J].岩石力学与工程学报,2010,29(2):417-422.(TANG Xiao-wu,ZHU Ji,LIU Wei,et al.Research on soil deformation during shield construction process[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(2):417-422.(in Chinese))
[14]梁荣柱,夏唐代,林存刚,等.盾构推进引起地表变形及深层土体水平位移分析[J].岩石力学与工程学报,2015,34(3):583-593.(LIANG Rong-zhu,XIA Tang-dai,LINCun-gang,et al.Analysis of ground surface displacement and horizontal movement of deep soils induced by shield advancing[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(3):583-593.(in Chinese))
[15]傅鹤林,李鲒,王洪涛,等.基于随机介质理论的浅埋偏压隧道沉降预测[J].铁道工程学报,2017,34(9):70-76.(FU He-lin,LI Jie,WANG Hong-tao,et al.Research on the ground settlement prediction in shallow tunnel under unsymmetrical pressure based on stochastic medium theory,Journal of Railway Engineering Society,2017,34(9):70-76.(in Chinese))
[16]NG C W W,LU H,PENG S Y.Three-dimensional centrifuge modelling of the effects of twin tunnelling on an existing pile[J].Tunnelling and Underground Space Technology,2013,35(4):189-199.
[17]NG C W W,LU H.Effects of the construction sequence of twin tunnels at different dept on an existing pile[J].Canadian Geotechnical Journal,2014,51(2):173-183.
[18]DIVALL.Ground movements associated with twin-tunnel construction in clay[D].London:City University London,2013.
[19]WU B R,LEE C J.Ground movements and collapse mechanism induced by tunnelling in clayey soil[J].International Journal of Physical Modelling in Geotechnics,2003,4(4):15-29.
[20]马少坤,陈欣,吕虎,等.不同埋置位置隧道对群桩影响的离心模型试验[J].中国公路学报,2015,28(8):67-73.(MA Shao-kun,CHEN Xin,LU Hu,et al.Centrifuge modelling test of effects of tunnelling with different depths on pile group[J].China Journal of Highway and Transport,2015,28(8):67-3.(in Chinese))
[21]LEE C J,WU B R,CHEN H T,et al.Tunnel stability and arching effects during tunneling in soft clayey soil[J].Tunnelling and Underground Space Technology,2006,21(2):119-132.
[22]DAS R,SINGH P K,KAINTHOLA A,et al.Numerical analysis of surface subsidence in asymmetric parallel highway tunnels[J].Journal of Rock Mechanics and Geotechnical Engineering,2017,9(1):170-179.
[23]CHEN S L,GUI M W,YANG M C.Applicability of the principle of superposition in estimating ground surface settlement of twin-and quadruple-tube tunnels[J].Tunnelling and Underground Space Technology,2012,28(1):135-149.
[24]王剑晨,张顶立,张成平,等.浅埋暗挖隧道近距施工引起的上覆地铁结构变形分析[J].岩石力学与工程学报,2014,33(1):90-97.(WANG Jian-chen,ZHANG Ding-li,ZHANG Cheng-ping,et al.Analysis of structural deformation of overlying subway station induced by approaching tunnel excavation in shallow depth[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(1):90-97.(in Chinese))
[25]杨子奇,葛克水,李皓.北京地区浅埋隧道开挖引起地表沉降的研究[J].地下空间与工程学报,2016,12(增刊1):225-231.(YANG Zi-qi,GE Ke-shui,LI Hao.Research on the surface subsidence caused by shallow buried tunnel excavation in beijing area[J].Chinese Journal of Underground Space and Engineering,2016,12(S1):225-231.(in Chinese))
[26]OU C Y,HWANG R N,LAI W J.Surface settlement during shield tunnelling at CH218 in Taipei[J].Canadian Geotechnical Journal,1998,35(1):159-168.
[27]张路青,杨志法,吕爱钟.任意布置方式下两任意形状孔洞平面弹性问题的解析法研究[J].中国科学:地球科学,2000,30(5):509-518.(ZHANG Lu-qing,YANG Zhi-fa,LüAi-zhong.Analytical study on plane elastic problem of two random geometry tunnels[J].Science in China(Series D),2000,30(5):509-518.(in Chinese))
[28]KOOI C B,VERRUIJT A.Interaction of circular holes in an infinite elastic medium[J].Tunnelling and Underground Space Technology,2001,16(1):59-62.
[29]SOKOLNIKOFF I S.Mathematical theory of elasticity[M].New York:McGraw-Hill,1956.
[30]MUSKHELISHVILI N I.Mathematical theory of elasticity[M].Leyden:International Publishing,1954.
[31]GONZALEZ C,SAGASETA C.Patterns of soil deformations around tunnels-application to the extension of Madrid Metro[J].Computers and Geotechnics,2001,28(6):445-468.
[32]MA S,SHAO Y,LIU Y,et al.Responses of pipeline to side-by-side twin tunnelling at different depths:3D centrifuge tests and numerical modelling[J].Tunnelling and Underground Space Technology,2017,66:157-173.
[33]KOUKOUTAS S P,SOFIANOS A I.Settlements due to single and twin tube urban EPB shield tunnelling[J].Geotechnical and Geological Engineering,2015,33(3):487-510.
[34]FARGNOLI V,BOLDINI D,AMOROSI A.Twin tunnel excavation in coarse grained soils:observations and numerical back-predictions under free field conditions and in presence of a surface structure[J].Tunnelling and Underground Space Technology,2015,49(6):454-469.
[2]夏元友,陈春舒,BAKRI M,等.浅埋隧道开挖引起的土体水平位移分析[J].岩土力学,2015,36(2):354-360.(XIAYuan-you,CHEN Chun-su,BAKRI M,et al.Analysis of horizontal displacement of soil induced by shallow tunnel excavation[J].Rock and Soil Mechanics,2015,36(2):354-360.(in Chinese))
[3]楼晓明,郑俊杰,章荣军.隧道施工引起的地表变形数值模拟[J].铁道工程学报,2007,108(9):62-66.(LOUXiao-ming,ZHENG Jun-jie,ZHANG Rong-jun.Simulation of numerical values of surface deformation caused by tunnel construction[J].Journal of Railway Engineering Society,2007,108(9):62-66.(in Chinese))
[4]郑刚,张扶正,张天奇,等.盾构隧道开挖及补偿注浆对地层扰动影响的室内试验及数值模拟研究[J].岩土工程学报,2016,38(10):1741-1753.(ZHENG Gang,ZHANGFu-zheng,ZHANG Tian-qi,et al.Disturbance of shield tunnel excavation and compensation grouting to surrounding soil:laboratory tests and numerical simulations[J].Chinese Journal of Geotechnical Engineering,2016,38(10):1741-1753.(in Chinese))
[5]陈仁朋,齐立志,汤旅军,等.砂土地层盾构隧道开挖面被动破坏极限支护力研究[J].岩石力学与工程学报,2013,31(增刊1):2877-2882.(CHEN Ren-peng,QI Li-zhi,TANG Lü-jun,et al.Study of limit supporting force of excavation face's passive failure of shield tunnels in sand strata[J].Chinese Journal of Rock Mechanics and Engineering,2013,31(S1):2877-2882.(in Chinese))
[6]王俊,何川,胡瑞青,等.土压平衡盾构掘进对上软下硬地层扰动研究[J].岩石力学与工程学报,2017,36(4):953-963.(WANG Jun,HE Chuan,HU Rui-qing,et al.Soil disturbance induced by EPB shield tunnelling in upper-soft and lower-hard ground[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(4):953-963.(in Chinese))
[7]叶飞,苟长飞,陈治,等.盾构隧道同步注浆引起的地表变形分析[J].岩土工程学报,2014,36(4):618-624.(YEFei,GOU Chang-fei,CHEN Zhi,et al.Ground surface deformation caused by synchronous grouting of shield tunnels[J].Chinese Journal of Geotechnical Engineering,2014,36(4):618-624.(in Chinese))
[8]MO P Q,YU H S.Undrained cavity-contraction analysis for prediction of soil behavior around tunnels[J].International Journal of Geomechanics,2017,17(5):04016121.
[9]VERRUIJT A.A complex variable solution for a deforming circular tunnel in an elastic half-plane[J].International Journal for Numerical and Analytical Methods in Geomechanics,1997,21(21):77-89.
[10]韩凯航,张成平,王梦恕.浅埋隧道围岩应力及位移的显式解析解[J].岩土工程学报,2014,36(12):2253-2259.(HAN Kai-hang,ZHANG Cheng-ping,WANG Meng-shu.Explicit analytical solutions for stress and displacement of surrounding rock in shallow tunnels[J].Chinese Journal of Geotechnical Engineering,2014,36(12):2253-2259.(in Chinese))
[11]PARK K H.Elastic solution for tunneling-induced ground movements in clays[J].International Journal of Geomechanics,2004,4(4):310-318.
[12]BOBET A.Drained and undrained response of deep tunnels subjected to far-field shear loading[J].Tunnelling and Underground Space Technology,2010,25(1):21-31.
[13]唐晓武,朱季,刘维,等.盾构施工过程中的土体变形研究[J].岩石力学与工程学报,2010,29(2):417-422.(TANG Xiao-wu,ZHU Ji,LIU Wei,et al.Research on soil deformation during shield construction process[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(2):417-422.(in Chinese))
[14]梁荣柱,夏唐代,林存刚,等.盾构推进引起地表变形及深层土体水平位移分析[J].岩石力学与工程学报,2015,34(3):583-593.(LIANG Rong-zhu,XIA Tang-dai,LINCun-gang,et al.Analysis of ground surface displacement and horizontal movement of deep soils induced by shield advancing[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(3):583-593.(in Chinese))
[15]傅鹤林,李鲒,王洪涛,等.基于随机介质理论的浅埋偏压隧道沉降预测[J].铁道工程学报,2017,34(9):70-76.(FU He-lin,LI Jie,WANG Hong-tao,et al.Research on the ground settlement prediction in shallow tunnel under unsymmetrical pressure based on stochastic medium theory,Journal of Railway Engineering Society,2017,34(9):70-76.(in Chinese))
[16]NG C W W,LU H,PENG S Y.Three-dimensional centrifuge modelling of the effects of twin tunnelling on an existing pile[J].Tunnelling and Underground Space Technology,2013,35(4):189-199.
[17]NG C W W,LU H.Effects of the construction sequence of twin tunnels at different dept on an existing pile[J].Canadian Geotechnical Journal,2014,51(2):173-183.
[18]DIVALL.Ground movements associated with twin-tunnel construction in clay[D].London:City University London,2013.
[19]WU B R,LEE C J.Ground movements and collapse mechanism induced by tunnelling in clayey soil[J].International Journal of Physical Modelling in Geotechnics,2003,4(4):15-29.
[20]马少坤,陈欣,吕虎,等.不同埋置位置隧道对群桩影响的离心模型试验[J].中国公路学报,2015,28(8):67-73.(MA Shao-kun,CHEN Xin,LU Hu,et al.Centrifuge modelling test of effects of tunnelling with different depths on pile group[J].China Journal of Highway and Transport,2015,28(8):67-3.(in Chinese))
[21]LEE C J,WU B R,CHEN H T,et al.Tunnel stability and arching effects during tunneling in soft clayey soil[J].Tunnelling and Underground Space Technology,2006,21(2):119-132.
[22]DAS R,SINGH P K,KAINTHOLA A,et al.Numerical analysis of surface subsidence in asymmetric parallel highway tunnels[J].Journal of Rock Mechanics and Geotechnical Engineering,2017,9(1):170-179.
[23]CHEN S L,GUI M W,YANG M C.Applicability of the principle of superposition in estimating ground surface settlement of twin-and quadruple-tube tunnels[J].Tunnelling and Underground Space Technology,2012,28(1):135-149.
[24]王剑晨,张顶立,张成平,等.浅埋暗挖隧道近距施工引起的上覆地铁结构变形分析[J].岩石力学与工程学报,2014,33(1):90-97.(WANG Jian-chen,ZHANG Ding-li,ZHANG Cheng-ping,et al.Analysis of structural deformation of overlying subway station induced by approaching tunnel excavation in shallow depth[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(1):90-97.(in Chinese))
[25]杨子奇,葛克水,李皓.北京地区浅埋隧道开挖引起地表沉降的研究[J].地下空间与工程学报,2016,12(增刊1):225-231.(YANG Zi-qi,GE Ke-shui,LI Hao.Research on the surface subsidence caused by shallow buried tunnel excavation in beijing area[J].Chinese Journal of Underground Space and Engineering,2016,12(S1):225-231.(in Chinese))
[26]OU C Y,HWANG R N,LAI W J.Surface settlement during shield tunnelling at CH218 in Taipei[J].Canadian Geotechnical Journal,1998,35(1):159-168.
[27]张路青,杨志法,吕爱钟.任意布置方式下两任意形状孔洞平面弹性问题的解析法研究[J].中国科学:地球科学,2000,30(5):509-518.(ZHANG Lu-qing,YANG Zhi-fa,LüAi-zhong.Analytical study on plane elastic problem of two random geometry tunnels[J].Science in China(Series D),2000,30(5):509-518.(in Chinese))
[28]KOOI C B,VERRUIJT A.Interaction of circular holes in an infinite elastic medium[J].Tunnelling and Underground Space Technology,2001,16(1):59-62.
[29]SOKOLNIKOFF I S.Mathematical theory of elasticity[M].New York:McGraw-Hill,1956.
[30]MUSKHELISHVILI N I.Mathematical theory of elasticity[M].Leyden:International Publishing,1954.
[31]GONZALEZ C,SAGASETA C.Patterns of soil deformations around tunnels-application to the extension of Madrid Metro[J].Computers and Geotechnics,2001,28(6):445-468.
[32]MA S,SHAO Y,LIU Y,et al.Responses of pipeline to side-by-side twin tunnelling at different depths:3D centrifuge tests and numerical modelling[J].Tunnelling and Underground Space Technology,2017,66:157-173.
[33]KOUKOUTAS S P,SOFIANOS A I.Settlements due to single and twin tube urban EPB shield tunnelling[J].Geotechnical and Geological Engineering,2015,33(3):487-510.
[34]FARGNOLI V,BOLDINI D,AMOROSI A.Twin tunnel excavation in coarse grained soils:observations and numerical back-predictions under free field conditions and in presence of a surface structure[J].Tunnelling and Underground Space Technology,2015,49(6):454-469.