地层渐进成拱对浅埋隧道上覆土压力影响研究
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摘要
砂土及完整性较差、黏聚强度较小的破碎岩体中,浅埋隧道地层拱作用机制随地层变形发展而变化,受此影响隧道松动土压力也相应变化。常规方法忽略了地层拱不同阶段力学机制的不同,同时未考虑剪切面转动与大主应力旋转之间的相互关系,因此,不能解决浅埋隧道地层能否成拱、地层拱何时贯通至地表以及地层拱发展对隧道松动土压力影响等问题。针对这一情况,提出渐进地层拱力学模型以反映不同阶段地层拱的力学机制;其次,同时考虑主应力旋转、剪切面转动及二者相互关系,确定拱内土体应力分布;随后,优化了传统主应力偏转与地层差异沉降间的数学模型。在此基础上确定了渐进地层拱对隧道松动土压力的影响。改进方法结果与传统方法结果及试验结果的对比验证了改进方法的有效性与适用性。通过参数分析研究了隧道初始松动压力、随地层变形发展的松动压力以及地层拱贯通至地表时的极限变形等关键参数。最后,对下北山超大跨浅埋隧道的研究说明了改进方法的实用性。结论显示:(1)初始松动压力为初始松动区内土体重力,初始松动区范围不受覆跨比影响,而受地层强度影响,随内摩擦角增加而减小;(2)最大拱效应阶段以后,松动土压力随地层变形发展而增加,深埋、小跨度隧道(H/D≤2)增长速率较慢,反之较快;(3)极限变形随覆跨比、内摩擦角增加而增加,深埋、小跨度隧道地层拱效应更明显;(4)对于下北山隧道,初始地层拱存在,初始松动土压力为0.37σ_v~0,极限松动土压力为0.41σ_v~0,最终松动土压力为0.54σ_v~0,隧道变形应控制在5.7%以下避免地层拱贯通至地表。
For underground excavations in sand and blocky rock masses with low cohesive strength, the loosening pressure above a shallow tunnel varies with the developing ground deformation due to evolutions of ground arching. However, the normal ground arching method fails in determining the existence of the ground arch, resulting in critical deformation when the ground arch reaches the ground surface and the variation of the loosening pressure as a function of the developed arching effect. This paper presents a modified method by introducing a continuously developed ground arching mechanism. Rotations of the principal stress and the correlation between orientations of the principal stress and the shear surface are used to determine the stress state within the arch.Previous methods determining the rotation of the shear surface as a function of the ground deformation was also modified to better reflect the test results. On the basis of the above three steps, a modified method is proposed. Comparisons of the results among the previous methods, the proposed method and the experiments examined the validity of the proposed method. Parametric analysis studied the initial loosening pressure, the evolution of the loosening pressure and the critical deformation. A case study by the proposed method indicates its practical use. Some important conclusions are:(1) the initial loosening pressure comes from the weight of the ground within the arch. The area of the initial-loosening zone is independent on the cover-depth ratios. Instead, the area is controlled by the friction angle of the ground. Grounds with low friction angles tend to have large initial-loosening zone with a high initial loosening pressure;(2) the loosening pressure increases with the developing ground deformation, and a lower raising rate is found for a deeper, smaller tunnel( H/D≤2);(3) the critical deformation increases with the raising cover-depth ratio and the increasing friction angle, indicating that a stronger arching effect is expected in such grounds;(4) for Xiabeishan tunnel, the arching effect exists, the initial loosening pressure is 0.37σ_v~0, the critical value is 0.41σ_v~0, the ultimate is 0.54σ_v~0, and the critical relative deformation is 5.7%.
For underground excavations in sand and blocky rock masses with low cohesive strength, the loosening pressure above a shallow tunnel varies with the developing ground deformation due to evolutions of ground arching. However, the normal ground arching method fails in determining the existence of the ground arch, resulting in critical deformation when the ground arch reaches the ground surface and the variation of the loosening pressure as a function of the developed arching effect. This paper presents a modified method by introducing a continuously developed ground arching mechanism. Rotations of the principal stress and the correlation between orientations of the principal stress and the shear surface are used to determine the stress state within the arch.Previous methods determining the rotation of the shear surface as a function of the ground deformation was also modified to better reflect the test results. On the basis of the above three steps, a modified method is proposed. Comparisons of the results among the previous methods, the proposed method and the experiments examined the validity of the proposed method. Parametric analysis studied the initial loosening pressure, the evolution of the loosening pressure and the critical deformation. A case study by the proposed method indicates its practical use. Some important conclusions are:(1) the initial loosening pressure comes from the weight of the ground within the arch. The area of the initial-loosening zone is independent on the cover-depth ratios. Instead, the area is controlled by the friction angle of the ground. Grounds with low friction angles tend to have large initial-loosening zone with a high initial loosening pressure;(2) the loosening pressure increases with the developing ground deformation, and a lower raising rate is found for a deeper, smaller tunnel( H/D≤2);(3) the critical deformation increases with the raising cover-depth ratio and the increasing friction angle, indicating that a stronger arching effect is expected in such grounds;(4) for Xiabeishan tunnel, the arching effect exists, the initial loosening pressure is 0.37σ_v~0, the critical value is 0.41σ_v~0, the ultimate is 0.54σ_v~0, and the critical relative deformation is 5.7%.
引文
[1]BARTON N,LIEN R,LUNDE J.Engineering classification of rock masses for the design of tunnel support[J].Rock Mechanics and Rock Engineering,1974,6(4):189-236.
[2]TERZAGHI K.Theoretical soil mechanics[M].Hoboken:John Wiley&Sons Inc.,1943.
[3]宫全美,张润来,周顺华,等.基于颗粒椭球体理论的隧道松动土压力计算方法[J].岩土工程学报,2017,39(1):99-105.GONG Quan-mei,ZHANG Run-lai,ZHOU Shun-hua,et al.Method for calculating loosening earth pressure around tunnels based on ellipsoid theory of particle flows[J].Chinese Journal of Geotechnical Engineering,2017,39(1):99-105.
[4]TALIA S D S,MOHAMMED Z E B,GOPAL S P M.Estimation of the coefficient of lateral stress used in the calculation of loads on buried structures[C]//Geotechnical Frontiers 2017.Orlando,Florida:American Society of Civil Engineers,2017:233-142.
[5]陈若曦,朱斌,陈云敏,等.基于主应力轴旋转理论的修正Terzaghi松动土压力[J].岩土力学,2010,31(5):1402-1406.CHEN Ruo-xi,ZHU Bin,CHEN Yun-min,et al.Modified Terzaghi loozening earth pressure based on theory of main stress axes rotation[J].Rock and Soil Mechanics,2010,31(5):1402-1406.
[6]赖丰文,陈福全,万梁龙.考虑不完全土拱效应的浅层地基竖向应力计算[J].岩土力学,2018,39(7):2546-2554.LAI Feng-wen,CHEN Fu-quan,WAN Liang-long.Vertical stress calculation of shallow foundations based on partially developed soil arching effect[J].Rock and Soil Mechanics,2018,39(7):2546-2554.
[7]徐长节,梁禄钜,陈其志,等.考虑松动区内应力分布形式的松动土压力研究[J].岩土力学,2018,39(6):1927-1934.XU Chang-jie,LIANG Lu-ju,CHEN Qi-zhi,et al.Research on loosening earth pressure considering the patterns of stress distribution in loosening zone[J].Rock and Soil Mechanics,2018,39(6):1927-1934.
[8]HANDY R L.The arch in soil arching[J].Journal of Geotechnical Engineering,1985,111(3):302-318.
[9]HANDY R L.Anatomy of an error[J].Journal of Geotechnical and Geoenvironmental Engineering,2004,130(7):768-771.
[10]PAIK K H,SALGADO R.Estimation of active earth pressure against rigid retaining walls considering arching effects[J].Géotechnique,2003,53(7):643-653.
[11]IGLESIA G R,EINSTEIN H H,WHITMAN R V.Validation of centrifuge model scaling for soil systems via trapdoor tests[J].Journal of Geotechnical and Geoenvironmental Engineering,2011,137(11):1075-1089.
[12]CHEVALIER B,COMBE G,VILLARD P.Experimental and discrete element modeling studies of the trapdoor problem:influence of the macro-mechanical frictional parameters[J].Acta Geotechnica,2012,7(1):15-39.
[13]GUO P,ZHOU S.Arch in granular materials as a free surface problem[J].International Journal for Numerical and Analytical Methods in Geomechanics,2013,37(9):1048-1065.
[14]赵志国,王炳龙,韩高孝,等.基于非圆颗粒Trapdoor试验模拟土拱效应[J].华东交通大学学报,2015,32(4):78-84.ZHAO Zhi-guo,WANG Bing-long,HAN Gao-xiao,et al.Soil arching of trapdoor tests based on non-circular particles[J].Journal of East China Jiaotong University,2015,32(4):72-84.
[15]RUI R,VAN TOL F,XIA X L,et al.Evolution of soil arching:2D DEM simulations[J].Computers and Geotechnics,2016,73:199-209.
[16]RUI R,VAN TOL F,XIA Y Y,et al.Evolution of soil arching:2D analytical models[J].International Journal of Geomechanics,2018,18(6):04018056(1)-04018056(15).
[17]黎春林.盾构隧道施工松动土压力计算方法研究[J].岩土工程学报,2014,36(9):1714-1720.LI Chun-lin.Method for calculating loosening earth pressure during construction of shield tunnels[J].Chinese Journal of Geotechnical Engineering,2014,36(9):1714-1720.
[18]叶飞,樊康佳,宋京,等.基于不完全拱效应的隧道预处理机制与计算方法[J].岩石力学与工程学报,2017,36(6):1469-1478.YE Fei,FAN Kang-jia,SONG Jing,et al.The pretreatment mechanism of tunnel and its calculation methods based on the incomplete arch effect[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(6):1469-1478.
[19]汪成兵,朱合华.埋深对软弱隧道围岩破坏影响机制试验研究[J].岩石力学与工程学报,2010,29(12):2442-2448.WANG Cheng-bing,ZHU He-hua.Experimental study of influence mechanism of buried depth on surrounding rock failure of tunnel constructed in soft rock[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(12):2442-2448.
[20]IGLESIA G R,EINSTEIN H H,WHITMAN R V.Determination of vertical loading on underground structures based on an arching evolution concept[C]//Geo-Engineering for Underground Facilities.Reston,USA:Geo-Institute of ASCE,1999:495-506.
[21]EVANS H C.An examination of arching in granular soils[D].Massachusetts:Massachusetts Institute of Technology,1983.
[22]IGLESIA G R,EISTEIN H H,WHITMAN R V.Investigation of soil arching with centrifuge tests[J].Journal of Geotechnical and Geoenvironmental Engineering,2014,140(2):04013005(1)-04013005(13).
[23]COSTA Y D,ZORNBERG J G,BUENO B S,et al.Failure mechanisms in sand over a deep active trapdoor[J].Journal of Geotechnical and Geoenvironmental Engineering,2009,135(11):1741-1753.
[24]HAN J,WANG F,AL-NADDAF M,et al.Progressive development of two-dimensional soil arching with displacement[J].International Journal of Geomechanics,2017,17(12):04017112(1)-04017112(12).
[25]WONG R C K,KAISER P K.Performance assessment of tunnels in cohesionless soils[J].Journal of Geotechnical Engineering,1991,117(12):1880-1901.
[26]AHMADI A,SEYEDI HOSSEININIA E.An experimental investigation on stable arch formation in cohesionless granular materials using developed trapdoor test[J].Powder Technology,2018,330:137-146.
[27]MCCUE S W,HILL J M.Free surface problems for static Coulomb-Mohr granular solids[J].Mathematics and Mechanics of Solids,2005,10(6):651-672.
[28]FRANZA A.Tunnelling and its effects on piles and piled structures[D].Nottingham:University of Nottingham,2017.
[29]FRANZA A,MARSHALL A M,ZHOU B.Greenfield tunnelling in sands:the effects of soil density and relative depth[J].Géotechnique,2019,69(4):297-307.
[30]FRANZA A,MARSHALL A M,HAJI T,et al.Asimplified elastic analysis of tunnel-piled structure interaction[J].Tunnelling and Underground Space Technology,2017,61:104-121.
[31]HANSMIRE W H,CORDING E J.Performance of a soft ground tunnel on the Washington metro[C]//North American Rapid Excavation and Tunneling Conference Proceedings.Chicago,Illinois:[s.n.],1972.
[32]CORDING,E J,HANSMIRE W H.Displaceemnt around soft ground tunnels[C]//Proceedings of the Fifth Panamerican Conference on Soil Mechanics.Buenos Aires:[s.n.],1975.
[33]PECK R B.Deep excavation and tunnelling in soft ground[C]//Proceedings of the Seventh International Conference on Soil Mechanics and Foundation Engineering.Mexico City:[s.n.],1969.
[2]TERZAGHI K.Theoretical soil mechanics[M].Hoboken:John Wiley&Sons Inc.,1943.
[3]宫全美,张润来,周顺华,等.基于颗粒椭球体理论的隧道松动土压力计算方法[J].岩土工程学报,2017,39(1):99-105.GONG Quan-mei,ZHANG Run-lai,ZHOU Shun-hua,et al.Method for calculating loosening earth pressure around tunnels based on ellipsoid theory of particle flows[J].Chinese Journal of Geotechnical Engineering,2017,39(1):99-105.
[4]TALIA S D S,MOHAMMED Z E B,GOPAL S P M.Estimation of the coefficient of lateral stress used in the calculation of loads on buried structures[C]//Geotechnical Frontiers 2017.Orlando,Florida:American Society of Civil Engineers,2017:233-142.
[5]陈若曦,朱斌,陈云敏,等.基于主应力轴旋转理论的修正Terzaghi松动土压力[J].岩土力学,2010,31(5):1402-1406.CHEN Ruo-xi,ZHU Bin,CHEN Yun-min,et al.Modified Terzaghi loozening earth pressure based on theory of main stress axes rotation[J].Rock and Soil Mechanics,2010,31(5):1402-1406.
[6]赖丰文,陈福全,万梁龙.考虑不完全土拱效应的浅层地基竖向应力计算[J].岩土力学,2018,39(7):2546-2554.LAI Feng-wen,CHEN Fu-quan,WAN Liang-long.Vertical stress calculation of shallow foundations based on partially developed soil arching effect[J].Rock and Soil Mechanics,2018,39(7):2546-2554.
[7]徐长节,梁禄钜,陈其志,等.考虑松动区内应力分布形式的松动土压力研究[J].岩土力学,2018,39(6):1927-1934.XU Chang-jie,LIANG Lu-ju,CHEN Qi-zhi,et al.Research on loosening earth pressure considering the patterns of stress distribution in loosening zone[J].Rock and Soil Mechanics,2018,39(6):1927-1934.
[8]HANDY R L.The arch in soil arching[J].Journal of Geotechnical Engineering,1985,111(3):302-318.
[9]HANDY R L.Anatomy of an error[J].Journal of Geotechnical and Geoenvironmental Engineering,2004,130(7):768-771.
[10]PAIK K H,SALGADO R.Estimation of active earth pressure against rigid retaining walls considering arching effects[J].Géotechnique,2003,53(7):643-653.
[11]IGLESIA G R,EINSTEIN H H,WHITMAN R V.Validation of centrifuge model scaling for soil systems via trapdoor tests[J].Journal of Geotechnical and Geoenvironmental Engineering,2011,137(11):1075-1089.
[12]CHEVALIER B,COMBE G,VILLARD P.Experimental and discrete element modeling studies of the trapdoor problem:influence of the macro-mechanical frictional parameters[J].Acta Geotechnica,2012,7(1):15-39.
[13]GUO P,ZHOU S.Arch in granular materials as a free surface problem[J].International Journal for Numerical and Analytical Methods in Geomechanics,2013,37(9):1048-1065.
[14]赵志国,王炳龙,韩高孝,等.基于非圆颗粒Trapdoor试验模拟土拱效应[J].华东交通大学学报,2015,32(4):78-84.ZHAO Zhi-guo,WANG Bing-long,HAN Gao-xiao,et al.Soil arching of trapdoor tests based on non-circular particles[J].Journal of East China Jiaotong University,2015,32(4):72-84.
[15]RUI R,VAN TOL F,XIA X L,et al.Evolution of soil arching:2D DEM simulations[J].Computers and Geotechnics,2016,73:199-209.
[16]RUI R,VAN TOL F,XIA Y Y,et al.Evolution of soil arching:2D analytical models[J].International Journal of Geomechanics,2018,18(6):04018056(1)-04018056(15).
[17]黎春林.盾构隧道施工松动土压力计算方法研究[J].岩土工程学报,2014,36(9):1714-1720.LI Chun-lin.Method for calculating loosening earth pressure during construction of shield tunnels[J].Chinese Journal of Geotechnical Engineering,2014,36(9):1714-1720.
[18]叶飞,樊康佳,宋京,等.基于不完全拱效应的隧道预处理机制与计算方法[J].岩石力学与工程学报,2017,36(6):1469-1478.YE Fei,FAN Kang-jia,SONG Jing,et al.The pretreatment mechanism of tunnel and its calculation methods based on the incomplete arch effect[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(6):1469-1478.
[19]汪成兵,朱合华.埋深对软弱隧道围岩破坏影响机制试验研究[J].岩石力学与工程学报,2010,29(12):2442-2448.WANG Cheng-bing,ZHU He-hua.Experimental study of influence mechanism of buried depth on surrounding rock failure of tunnel constructed in soft rock[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(12):2442-2448.
[20]IGLESIA G R,EINSTEIN H H,WHITMAN R V.Determination of vertical loading on underground structures based on an arching evolution concept[C]//Geo-Engineering for Underground Facilities.Reston,USA:Geo-Institute of ASCE,1999:495-506.
[21]EVANS H C.An examination of arching in granular soils[D].Massachusetts:Massachusetts Institute of Technology,1983.
[22]IGLESIA G R,EISTEIN H H,WHITMAN R V.Investigation of soil arching with centrifuge tests[J].Journal of Geotechnical and Geoenvironmental Engineering,2014,140(2):04013005(1)-04013005(13).
[23]COSTA Y D,ZORNBERG J G,BUENO B S,et al.Failure mechanisms in sand over a deep active trapdoor[J].Journal of Geotechnical and Geoenvironmental Engineering,2009,135(11):1741-1753.
[24]HAN J,WANG F,AL-NADDAF M,et al.Progressive development of two-dimensional soil arching with displacement[J].International Journal of Geomechanics,2017,17(12):04017112(1)-04017112(12).
[25]WONG R C K,KAISER P K.Performance assessment of tunnels in cohesionless soils[J].Journal of Geotechnical Engineering,1991,117(12):1880-1901.
[26]AHMADI A,SEYEDI HOSSEININIA E.An experimental investigation on stable arch formation in cohesionless granular materials using developed trapdoor test[J].Powder Technology,2018,330:137-146.
[27]MCCUE S W,HILL J M.Free surface problems for static Coulomb-Mohr granular solids[J].Mathematics and Mechanics of Solids,2005,10(6):651-672.
[28]FRANZA A.Tunnelling and its effects on piles and piled structures[D].Nottingham:University of Nottingham,2017.
[29]FRANZA A,MARSHALL A M,ZHOU B.Greenfield tunnelling in sands:the effects of soil density and relative depth[J].Géotechnique,2019,69(4):297-307.
[30]FRANZA A,MARSHALL A M,HAJI T,et al.Asimplified elastic analysis of tunnel-piled structure interaction[J].Tunnelling and Underground Space Technology,2017,61:104-121.
[31]HANSMIRE W H,CORDING E J.Performance of a soft ground tunnel on the Washington metro[C]//North American Rapid Excavation and Tunneling Conference Proceedings.Chicago,Illinois:[s.n.],1972.
[32]CORDING,E J,HANSMIRE W H.Displaceemnt around soft ground tunnels[C]//Proceedings of the Fifth Panamerican Conference on Soil Mechanics.Buenos Aires:[s.n.],1975.
[33]PECK R B.Deep excavation and tunnelling in soft ground[C]//Proceedings of the Seventh International Conference on Soil Mechanics and Foundation Engineering.Mexico City:[s.n.],1969.