基于随机场理论的盾构隧道地表变形分析

doi:10.13722/j.cnki.jrme.2016.0099

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摘要采用随机场理论和数值分析相结合的方法，研究土性参数的空间变异性对盾构隧道施工地表变形的影响。利用协方差矩阵分解法建立描述土性参数空间变异性特征的随机场模型，结合Monte-Carlo策略，采用FLAC3D软件分析弹性模量的变异系数、相关距离对地表变形的影响。研究结果表明：土体弹性模量的空间变异性对地表变形规律有着重要的影响，在变形形态和量值上均有不同程度的体现；根据土体弹性模量的相关距离与隧道直径之间比值的大小关系，总结提出3种地表变形模式；最大地表沉降近似服从对数正态分布，且随着土体弹性模量的变异系数和相关距离的增大，最大地表沉降的概率分布越分散，超出沉降监测控制值的概率逐渐增加。

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	程红战
	陈健
	李健斌
	胡之锋
	李建贺
	黄珏皓

关键词 ：隧道工程, 盾构隧道, 随机场, 空间变异性, 地表变形, 概率分析

Abstract：Random field theory and numerical analysis method are combined to investigate the influence of the spatial variability of material properties on surface deformation caused by shield tunneling. Random fields of elasticity modulus are generated by Covariance Matrix Decomposition method to model the characteristics of spatial variability. Within Monte-Carlo framework，FLAC3D is used to analyze the influence of coefficient of variation and correlation distance of elasticity modulus on surface deformation. The results show the spatial variability of elasticity modulus has significant effects on both the values of greenfield settlement and the shapes of settlement trough. Depending on the relative size ratio between correlation distance and tunnel diameter，three surface deformation patterns are identified. The distribution of maximum surface settlement follows an approximate lognormal distribution. With coefficient of variation and correlation distance increasing，the more scattered the probability distribution of the maximum surface settlement，and the larger the probability of surface settlement exceeding the critical value.

Key words： tunnelling engineering shield tunnel random field spatial variability surface deformation probability analysis

引用本文:

程红战，陈健，李健斌，胡之锋，李建贺，黄珏皓. 基于随机场理论的盾构隧道地表变形分析[J]. 岩石力学与工程学报, 2016, 35(S2): 4256-4264.
CHENG Hongzhan，CHEN Jian，LI Jianbin，HU Zhifeng，LI Jianhe，HUANG Juehao. Study on surface deformation induced by shield tunneling based on random field theory. , 2016, 35(S2): 4256-4264.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2016.0099 或 https://rockmech.whrsm.ac.cn/CN/Y2016/V35/IS2/4256

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[14]	丁春林，朱世友，周顺华. 地应力释放对盾构隧道围岩稳定性和地表沉降变形的影响[J]. 岩石力学与工程学报，2002，21(11)：1 633-1 638.(DING Chunlin，ZHU Shiyou，ZHOU Shunhua. Influence of in-situ stress release on the stability of surrounding rock masses and ground surface settlement for shield-driven tunnel[J]. Chinese Journalof Rock Mechanics and Engineering，2002，21(11)：1 633-1 638.(in Chinese))
[1]	刘招伟，王梦恕，董新平. 地铁隧道盾构法施工引起的地表沉降分析[J]. 岩石力学与工程学报，2003，22(8)：1 297-1 301.(LIU Zhaowei，WANG Mengshu，DONG Xinping. Analysis of ground surface settlement of metro tunnel induced by shield construction[J]. ChineseJournal of Rock Mechanics and Engineering，2003，22(8)：1 297-1 301.(in Chinese))
[15]	ROWE R K，LEE K M. Subsidence owing to tunnelling. II. Evaluation of a prediction technique[J]. Canadian Geotechnical Journal，1992，29(6)：941-954.
[2]	PECK R B. Deep excavations and tunnelling in soft ground[C]// Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering. Mexico：Sociedad Mexicana de Mecanicade Suelos，A. C.，1969：225-290.
[16]	LUMB P. The variability of natural soils[J]. Canadian Geotechnical Journal，2011，3(2)：74-97.
[3]	ATTEWELL P B，WOODMAN J P. Predicting the dynamics of ground settlement and its derivatives caused by tunnelling in soil[J]. Ground Engineering，1982，15(8)：13-20.
[17]	VANMARCKE E H. Probabilistic modeling of soil profiles[J]. Journal of the Geotechnical Engineering Division，1977，103：1227-1246.
[4]	O'REILLY M P，NEW B M. Settlements above tunnels in the United Kingdom-their magnitude and prediction[C]// Proceedings of the Tunnelling'82. [S.1.]：[s.n.]，1982：173-181.
[18]	VANMARCKE E H. Random fields：analysis and synthesis[M]. Cambridge：MIT Press，1983：1-382.
[5]	MAIR R J，TAYLOR R N，BRACEGIRDLE A. Subsurface settlement profiles above tunnels in clays[J]. Géotechnique，1995，45(2)：315-320.
[19]	GRIFFITHS D V，HUANG J S，FENTON G A. Influence of spatial variability on slope reliability using 2D random fields[J]. Journal of Geotechnicaland Geoenvironmental Engineering，2009，135(10)：1367-1378.
[6]	SAGASETA C. Analysis of undrained soil deformation due to ground loss[J]. Geotechnique，1988，38(3)：301-320.
[20]	FENTON G A，GRIFFITHS D V，FENTON G A. Bearing-capacity prediction of spatially random c-φsoils[J]. Canadian Geotechnical Journal，2003，40(1)：54-65.
[7]	VERRUIJT A，BOOKER J R. Surface settlements due to deformation of a tunnel in an elastic half plane[J]. Geotechnique，1996，46(4)：753-756.
[21]	BAKER J W. Liquefaction riskassessment using geostatistics to account for soil spatial variability[J]. Journal of Geotechnical andGeoenvironmental Engineering，2008，134(1)：14-23.
[8]	LOGANATHANN，POULOSHG. Analytical prediction for tunneling-induced ground movements in clays[J]. Journal of Geotechnical and Geoenvironmental Engineering，1998，124(9)：846-856.
[22]	ESHRAGHI A，ZARE S. Face Stability evaluation of a TBM-driven tunnel in heterogeneous soil using a probabilistic approach[J]. International Journal of Geomechanics，2014，15(6)：04014095.
[9]	GUTTLER U，STOFFERSU. Investigation of the deformation and collapse behaviour of circular lined tunnels in centrifuge model tests[C]// Centrifuges in Soil Mechanics. Rotterdam，Balkema：[s.n.]，1988：183-186.
[23]	MOLLON G，DIAS D，SOUBRA A H. Probabilistic analyses of tunneling-induced ground movements[J]. Acta Geotechnica，2013，8(2)：181-199.
[10]	IMAMURA S，HAGIWARA T，MITO K，et al. Settlement trough above a model shield observed in a centrifuge[J]. Centrifuge，1998，98：23-25.
[24]	MIROS，KÖNIG M，HARTMANN D，et al. A probabilistic analysis of subsoil parameters uncertainty impacts on tunnel-induced ground movements with a back-analysis study[J]. Computers and Geotechnics，2015，68：38-53.
[11]	GRANT R J，TAYLOR R N. Centrifuge modelling of ground movements due to tunnelling in layered ground[C]//Proceedings of theInt. Sympos. on Geotechnical Aspects of Underground Constructionin Soft Ground. [S.l.]：[s.n.]，1996：507-512.
[25]	DAVIS M W. Production of conditional simulations via the LU triangular decomposition of the covariance matrix[J]. Mathematical Geology，1987，19(2)：91-98.
[12]	周小文，濮家骝. 砂土中隧洞开挖引起的地面沉降试验研究[J]. 岩土力学，2002，23(5)：1 074-1 079.(ZHOU Xiaowen，PU Jialiu. Centrifuge model test on ground settlement induced by tunneling in sandy soil[J]. Rock and Soil Mechanics，2002，23(5)：1 074-1 079. (in Chinese))
[26]	张继周，缪林昌. 岩土参数概率分布类型及其选择标准[J]. 岩石力学与工程学报，2009，28(增 2)：3527-3532.(ZHANG Jizhou，MIAO Linchang. Types and selection criteria of probabilitydistribution of rock and soilparameters[J]. Chinese Journal of RockMechanics and Engineering，2009，28(Supp.2)：3527-3532.(inChinese))
[13]	朱合华，徐前卫，廖少明，等. 土压平衡盾构法施工参数的模型试验研究[J]. 岩土工程学报，2006，25(5)：553-557.(ZHU Hehua，XU Qianwei，LIAO Shaoming，et al. Experimental study on working parameters of EPB shield machine[J]. Chinese Journal of Geotechnical Engineering，2006，25(5)：553-557.(in Chinese))
[27]	张传庆，冯夏庭，周辉，等. 应力释放法在隧洞开挖模拟中若干问题的研究[J]. 岩土力学，2008，29(5)：1 174-1 181.(ZHANG Chuanqing，FENG Xiating，ZHOU Hui，et al. Study of some problems about application of stress release method to tunnel excavation simulation[J]. Rock and Soil Mechanics，2008，29(5)：1 174-1 181. (in Chinese))
[14]	丁春林，朱世友，周顺华. 地应力释放对盾构隧道围岩稳定性和地表沉降变形的影响[J]. 岩石力学与工程学报，2002，21(11)：1 633-1 638.(DING Chunlin，ZHU Shiyou，ZHOU Shunhua. Influence of in-situ stress release on the stability of surrounding rock masses and ground surface settlement for shield-driven tunnel[J]. Chinese Journalof Rock Mechanics and Engineering，2002，21(11)：1 633-1 638.(in Chinese))
[28]	程勇刚，常晓林，李典庆. 考虑岩体空间变异性的隧洞围岩变形随机分析[J]. 岩石力学与工程学报，2012，31(增1)：2 767-2 775. (CHENGYonggang，CHANG Xiaolin，LI Dianqing. Deformation stochastic analysis of tunnel surrounding rock considering its spatialrandomness[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(Supp.1)：2 767-2 775.(in Chinese))
[15]	ROWE R K，LEE K M. Subsidence owing to tunnelling. II. Evaluation of a prediction technique[J]. Canadian Geotechnical Journal，1992，29(6)：941-954.
[29]	FENTON G A，GRIFFITHS D V. Probabilistic foundation settlement on spatially random soil[J]. Journal of Geotechnical andGeoenvironmental Engineering，2002，128(5)：381-390.
[16]	LUMB P. The variability of natural soils[J]. Canadian Geotechnical Journal，2011，3(2)：74-97.
[30]	FENTON G A，GRIFFITHS D V. Three-dimensional probabilistic foundation settlement[J]. Journal of Geotechnical andGeoenvironmental Engineering，2005，131(2)：232-239.
[17]	VANMARCKE E H. Probabilistic modeling of soil profiles[J]. Journal of the Geotechnical Engineering Division，1977，103：1227-1246.
[18]	VANMARCKE E H. Random fields：analysis and synthesis[M]. Cambridge：MIT Press，1983：1-382.
[19]	GRIFFITHS D V，HUANG J S，FENTON G A. Influence of spatial variability on slope reliability using 2D random fields[J]. Journal of Geotechnicaland Geoenvironmental Engineering，2009，135(10)：1367-1378.
[20]	FENTON G A，GRIFFITHS D V，FENTON G A. Bearing-capacity prediction of spatially random c-φsoils[J]. Canadian Geotechnical Journal，2003，40(1)：54-65.
[21]	BAKER J W. Liquefaction riskassessment using geostatistics to account for soil spatial variability[J]. Journal of Geotechnical andGeoenvironmental Engineering，2008，134(1)：14-23.
[22]	ESHRAGHI A，ZARE S. Face Stability evaluation of a TBM-driven tunnel in heterogeneous soil using a probabilistic approach[J]. International Journal of Geomechanics，2014，15(6)：04014095.
[23]	MOLLON G，DIAS D，SOUBRA A H. Probabilistic analyses of tunneling-induced ground movements[J]. Acta Geotechnica，2013，8(2)：181-199.
[24]	MIROS，KÖNIG M，HARTMANN D，et al. A probabilistic analysis of subsoil parameters uncertainty impacts on tunnel-induced ground movements with a back-analysis study[J]. Computers and Geotechnics，2015，68：38-53.
[25]	DAVIS M W. Production of conditional simulations via the LU triangular decomposition of the covariance matrix[J]. Mathematical Geology，1987，19(2)：91-98.
[26]	张继周，缪林昌. 岩土参数概率分布类型及其选择标准[J]. 岩石力学与工程学报，2009，28(增 2)：3527-3532.(ZHANG Jizhou，MIAO Linchang. Types and selection criteria of probabilitydistribution of rock and soilparameters[J]. Chinese Journal of RockMechanics and Engineering，2009，28(Supp.2)：3527-3532.(inChinese))
[27]	张传庆，冯夏庭，周辉，等. 应力释放法在隧洞开挖模拟中若干问题的研究[J]. 岩土力学，2008，29(5)：1 174-1 181.(ZHANG Chuanqing，FENG Xiating，ZHOU Hui，et al. Study of some problems about application of stress release method to tunnel excavation simulation[J]. Rock and Soil Mechanics，2008，29(5)：1 174-1 181. (in Chinese))
[28]	程勇刚，常晓林，李典庆. 考虑岩体空间变异性的隧洞围岩变形随机分析[J]. 岩石力学与工程学报，2012，31(增1)：2 767-2 775. (CHENGYonggang，CHANG Xiaolin，LI Dianqing. Deformation stochastic analysis of tunnel surrounding rock considering its spatialrandomness[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(Supp.1)：2 767-2 775.(in Chinese))
[29]	FENTON G A，GRIFFITHS D V. Probabilistic foundation settlement on spatially random soil[J]. Journal of Geotechnical andGeoenvironmental Engineering，2002，128(5)：381-390.
[30]	FENTON G A，GRIFFITHS D V. Three-dimensional probabilistic foundation settlement[J]. Journal of Geotechnical andGeoenvironmental Engineering，2005，131(2)：232-239.