基于主应力旋转特征的浅埋隧道上覆土压力计算及不完全拱效应分析
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摘要
砂土及黏聚强度较低的破碎岩体中,不完全拱效应对浅埋隧道上覆土压力计算的影响尚不明确。不同于传统极限平衡方法考虑主应力迹线的分布形态,直接考虑隧道开挖后主应力旋转角的分布特征,同时考虑滑移面范围变化及滑移面摩擦角调用情况,改进了浅埋隧道上覆土压力的计算。在此基础上分析完全拱作用下土体平均侧压力系数、竖向应力分布等特点,并与传统方法比较说明了其异同。此外,与数值结果、模型试验结果对比验证了改进解的适用性。最后在改进解基础上分析不完全拱效应的影响。结论显示:(1)隧道开挖后,滑移面范围内土体竖向应力减少,转移至滑移面外稳定土体,滑移面附近剪切应力δ集中,阻碍隧道上方土体向下变形,改进方法计算所得应力分布与实际情况更相符;(2)平均侧压力系数K_w~(av)受土体内摩擦角φ及滑移面调用摩擦角δ共同影响,土体内摩擦角较小时,可忽略不完全拱效应δ/φ对平均侧压力系数的影响;(3)改进解与传统解均表明地层拱作用效果系数K_w~(av)tanδ在一定范围内对土体内摩擦角φ不敏感;(4)此外,改进解表明地层拱作用效果系数K_w~(av)tanδ对土体内摩擦角φ的不敏感性除受φ取值范围影响外,还受不完全拱效应δ/φ影响,随不完全拱效应增强(δ/φ减小),K_w~(av)tanδ对φ的不敏感性越来越明显。
For shallow tunnels in sand or some poor blocky rock masses with a very low cohesive,effect of the partially mobilized arching on the calculation of the overburden pressure is still not well understood.a modified approach,different from previous limit equilibrium methods that calculate the vertical loading by the assumption of the trace of the principal stress,was proposed taking into account the distribution of the rotation angle of the principal stress,the variation of the slip surface and the friction angle mobilized on the slip surface.The average lateral stress coefficient and the distribution of the vertical stress above the tunnel were analyzed by the modified approach and were compared with those obtained by previous limit equilibrium methods.The modified approach was verified by numerical simulation and experimental results,and the partially mobilized arching effects were analyzed.The results show that,after tunnel excavation,the vertical stress within and outside of the range of the slip surface decreases and increases respectively,and that the shear stress near the slip surface is mobilized to prevent the soil above the tunnel from slipping.The average lateral stress coefficientK_w~(av) is a function of the soil friction angle and the friction angle mobilized on the slip surface.The partially mobilized arching effectsδ/φ on the average lateral stress coefficientK_w~(av) can be ignored when the soil friction angle φ is low.It is also shown that the ground arching effectK_w~(av)tanδcalculated by the modified approach and previous methods are all insensitive to φ within a range of φ .The insensitivity ofK_w~(av)tanδto φ is not only affected by φ but also affected by the partially arching effectδ/φ .The lower the friction angle mobilized on the slip surface,the more distinct the insensitivity is.
For shallow tunnels in sand or some poor blocky rock masses with a very low cohesive,effect of the partially mobilized arching on the calculation of the overburden pressure is still not well understood.a modified approach,different from previous limit equilibrium methods that calculate the vertical loading by the assumption of the trace of the principal stress,was proposed taking into account the distribution of the rotation angle of the principal stress,the variation of the slip surface and the friction angle mobilized on the slip surface.The average lateral stress coefficient and the distribution of the vertical stress above the tunnel were analyzed by the modified approach and were compared with those obtained by previous limit equilibrium methods.The modified approach was verified by numerical simulation and experimental results,and the partially mobilized arching effects were analyzed.The results show that,after tunnel excavation,the vertical stress within and outside of the range of the slip surface decreases and increases respectively,and that the shear stress near the slip surface is mobilized to prevent the soil above the tunnel from slipping.The average lateral stress coefficientK_w~(av) is a function of the soil friction angle and the friction angle mobilized on the slip surface.The partially mobilized arching effectsδ/φ on the average lateral stress coefficientK_w~(av) can be ignored when the soil friction angle φ is low.It is also shown that the ground arching effectK_w~(av)tanδcalculated by the modified approach and previous methods are all insensitive to φ within a range of φ .The insensitivity ofK_w~(av)tanδto φ is not only affected by φ but also affected by the partially arching effectδ/φ .The lower the friction angle mobilized on the slip surface,the more distinct the insensitivity is.
引文
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[20]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):1 075-1 089.
[21]ZHANG H,ZHANG P,ZHOU W,et al.A new model to predict soil pressure acting on deep burial jacked pipes[J].Tunnelling and Underground Space Technology,2016,60(Supp.C):183-196.
[22]PAIK K H,SALGADO R.Estimation of active earth pressure against rigid retaining walls considering arching effects[J].Géotechnique,2003,53(53):643-653.
[23]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):2 442-2 448.(WANGChengbin,ZHU Hehua.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):2 442-2 448.(in Chinese))
[24]DA SILVA T S,ELSHAFIE M Z E B,MADABHUSHI G S P.Estimation of the coefficient of lateral stress used in the calculation of loads on buried structures[C]//Proceedings of Geotechnical Frontiers2017.Orlando,Florida.Reston,Virginia:American Society of Civil Engineers,2017:233-242.
[25]HANDY R L.Anatomy of an error[J].Journal of Geotechnical and Geoenvironmental Engineering,2004,130(7):768-771.
[26]PAIK K,SAGONG M,LEE H.Analysis of active earth pressure against rigid caissons backfilled with crushed rock and sand[J].Canadian Geotechnical Journal,2009,46(10):1 216-1 228.
[27]WONG R C K,KAISER P K.Performance assessment of tunnels in Cohesionless soils[J].Journal of Geotechnical Engineering,1991,117(12):1 880-1 901.
[28]CHEN R P,TANG L J,YIN X S,et al.An improved 3D wedge-prism model for the face stability analysis of the shield tunnel in cohesionless soils[J].Acta Geotechnica,2015,10(5):683-692.
[29]SINGH S,SIVAKUGAN N,SHUKLA S K.Can soil arching be insensitive toφ?[J].International Journal of Geomechanics,2010,10(3):124-128.
[2]TERZAGHI K.Theoretical soil mechanics[M].Hoboken,NJ,USA:John Wiley and Sons,Inc.,1943:66-76.
[3]BARTON N,LIEN R,LUNDE J.Engineering classification of rock masses for the design of tunnel support[J].Rock Mechanics Felsmechanik Mcanique des Roches,1974,6(4):189-236.
[4]KRYNINE D P.Discussion of stability and stiffness of cellular cofferdams′by Karl Terzaghi[J].Transactions of the American Society of Civil Engineers,1945,110(1):1 120-1 186.
[5]HANDY R L.The arch in soil arching[J].Journal of Geotechnical Engineering,1985,111(3):302-318.
[6]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):1 402-1 406.(CHEN Ruoxi,ZHU Bin,CHEN Yunmin,et al.Modified Terzaghi loozening earth pressure based on theory of main stress axes rotation[J].Rock and Soil Mechanics,2010,31(5):1 402-1 406.(in Chinese))
[7]宋玉香,贾晓云,朱永全.地铁隧道竖向土压力荷载的计算研究[J].岩土力学,2007,28(10):2 240-2 244.(SONG Yuxiang,JIAXiaoyun,ZHU Yongquan.Study on vertical earth pressure calculation of metro tunnel[J].Rock and Soil Mechanics,2007,28(10):2 240-2 244.(in Chinese))
[8]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):1 714-1 720.(LI Chunlin.Method for calculating loosening earth pressure during construction of shield tunnels[J].Chinese Journal of Geotechnical Engineering,2014,36(9):1 714-1 720.(in Chinese))
[9]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.(GONGQuanmei,ZHANG Runlai,ZHOU Shunhua,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.(in Chinese))
[10]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):1 469-1 478.(YE Fei,FAN Kangjia,SONG Jing,et al.The pretreatment mechanism of tunnels and its calculation method based on the incomplete arch effect[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(6):1 469-1 478.(in Chinese))
[11]ADACHI T,KIMURA M,KISHIDA K.Experimental study on the distribution of earth pressure and surface settlement through threedimensional trapdoor tests[J].Tunnelling and Underground Space Technology,2003,18(2):171-183.
[12]CHEN K H,PENG F L.An improved method to calculate the vertical earth pressure for deep shield tunnel in Shanghai soil layers[J].Tunnelling and Underground Space Technology,2018,75:43-66.
[13]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.
[14]IGLESIA G R,EINSTEIN H H,WHITMAN R V.Determination of vertical loading on underground structures based on an arching evolution concept[C]//Proceedings of the Geo-engineering for Underground Facilities.Iglesia,Geraldo:[s.n.],1999:495-506.
[15]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):1 741-1 753.
[16]EVANS H C.An examination of arching in granular soils[M.S.Thesis][D].Cambridge,Massachusetts,U.S.:Massachusetts Institute of Technology,1983.
[17]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):4017112.
[18]LADANYI B,HOYAUX B.A study of the trap-door problem in a granular mass[J].Canadian Geotechnical Journal,1969,6(1):1-14.
[19]GERALDO R I,HERBERT H E,ROBERT V W.Investigation of soil arching with centrifuge tests[J].Journal of Geotechnical and Geoenvironmental Engineering,2014,140(2):4013005.
[20]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):1 075-1 089.
[21]ZHANG H,ZHANG P,ZHOU W,et al.A new model to predict soil pressure acting on deep burial jacked pipes[J].Tunnelling and Underground Space Technology,2016,60(Supp.C):183-196.
[22]PAIK K H,SALGADO R.Estimation of active earth pressure against rigid retaining walls considering arching effects[J].Géotechnique,2003,53(53):643-653.
[23]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):2 442-2 448.(WANGChengbin,ZHU Hehua.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):2 442-2 448.(in Chinese))
[24]DA SILVA T S,ELSHAFIE M Z E B,MADABHUSHI G S P.Estimation of the coefficient of lateral stress used in the calculation of loads on buried structures[C]//Proceedings of Geotechnical Frontiers2017.Orlando,Florida.Reston,Virginia:American Society of Civil Engineers,2017:233-242.
[25]HANDY R L.Anatomy of an error[J].Journal of Geotechnical and Geoenvironmental Engineering,2004,130(7):768-771.
[26]PAIK K,SAGONG M,LEE H.Analysis of active earth pressure against rigid caissons backfilled with crushed rock and sand[J].Canadian Geotechnical Journal,2009,46(10):1 216-1 228.
[27]WONG R C K,KAISER P K.Performance assessment of tunnels in Cohesionless soils[J].Journal of Geotechnical Engineering,1991,117(12):1 880-1 901.
[28]CHEN R P,TANG L J,YIN X S,et al.An improved 3D wedge-prism model for the face stability analysis of the shield tunnel in cohesionless soils[J].Acta Geotechnica,2015,10(5):683-692.
[29]SINGH S,SIVAKUGAN N,SHUKLA S K.Can soil arching be insensitive toφ?[J].International Journal of Geomechanics,2010,10(3):124-128.