地下隧洞工程弹性反演唯一性的探讨
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摘要
对于地下隧洞工程,依据完备的量测信息开展弹性反分析,可望唯一反演确定岩土力学参数。文章利用平面弹性复变方法和一般弹性理论推导出任意形状隧洞的位移、应力解析表达式;基于隧洞围岩位移、应力解析解,依据参数可辨识条件探讨了地下隧洞工程弹性反演参数的唯一性,并通过算例进行了验证。研究表明,依据完备的量测信息开展弹性反分析,只要测点布置方式适当,反演参数满足相应的限定条件,五个参数(σv、σh、τ、E、μ)和同时反演具有唯一性。参数反演唯一性对参数的限制条件及对测点布置方式的要求受隧洞形状复杂性的影响,随着隧洞复杂性的提高对参数的限制条件大为减少,对测点布置方式的要求也会降低。算例结果表明,结论是正确的。
Utilizing the complete measured information to perform elastic back-analysis,all mechanical parameters may be determined uniquely in tunnel engineering.Via planar elastic complex variable technique and general elastic theory,the analytic formulas of displacements and stresses were derived.Based on the displacement and disturbed stress solutions for plane elasticity problems,this paper studies the inversion uniqueness of parameters according to the differentiability condition of parameters,and uses a simple example to validate the conclusion.The study shows,based on the complete measured information,the elastic inversion of the five parameters is unique on condition that the arrangement of measuring points is appropriate and the parameters satisfy the restrictive conditions.The restrictive conditions and the required arrangement are influenced by the shape complexity of tunnel,and with the shape complexity of tunnel increasing,the restrictive conditions of the parameters are decreased,and the requirement for the arrangement of the measuring points is reduced.Results of an example indicated the validity of the conclusions.
Utilizing the complete measured information to perform elastic back-analysis,all mechanical parameters may be determined uniquely in tunnel engineering.Via planar elastic complex variable technique and general elastic theory,the analytic formulas of displacements and stresses were derived.Based on the displacement and disturbed stress solutions for plane elasticity problems,this paper studies the inversion uniqueness of parameters according to the differentiability condition of parameters,and uses a simple example to validate the conclusion.The study shows,based on the complete measured information,the elastic inversion of the five parameters is unique on condition that the arrangement of measuring points is appropriate and the parameters satisfy the restrictive conditions.The restrictive conditions and the required arrangement are influenced by the shape complexity of tunnel,and with the shape complexity of tunnel increasing,the restrictive conditions of the parameters are decreased,and the requirement for the arrangement of the measuring points is reduced.Results of an example indicated the validity of the conclusions.
引文
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[6]张路青,贾正雪.弹性位移反分析对地应力、弹模的反演唯一性[J].岩土工程学报,2001,23(2):172~177Zhang Luqing,Jia ZhengXue.Inversion Uniqueness of Elastic Displacement Back-analysis for Ground Stress,Elastic Modulus andPoisson's Ratio[J].Chinese Journal of Geotechnical Engineering,2001,23(2):172~177(in Chinese)
[7]杨志法,王思敬,冯紫良,等.岩土工程反分析原理及应用[M].北京:地震出版社,2003Yang Zhifa,Wang Sijing,Feng Ziliang,etc.al.Principle and Application of Back-analysis in Geotechical Engineering[M].Bei-jing:Earthquake Press,2003(in Chinese)
[8]王登刚,刘迎曦,李守巨,等.巷道围岩初始应力场和弹性模量的区间反演方法[J].岩石力学与工程学报,2002,21(3):305~308Wang Denggang,Liu Yingxi,Li Shouju,etc.al.Interval Back Analysis on Initial Stresses and Elastic Modulus of SurroundingRocks of Tunnels[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(3):305~308(in Chinese)
[9]吴祥松,朱合华,叶飞.岩土工程参数反分析的可辨识性研究[J].地下空间与工程学报,2006,2(3):377~379Wu Xiangsong,Zhu Hehua,Ye Fei.Research on Identifiability of the Parameter in the Back Analysis of Geotechnical EngineeringProblems[J].Chinese Journal of Underground Space and Engineering,2006,2(3):377~379(in Chinese))
[10]袁鸿鹄,李云鹏,唐明明,等.山岭隧道围岩流变参数识别及应用研究[J].现代隧道技术,2009,46(5):61~65Yuan Honghu,Li Yunpeng,Tang Mingming,etc al.Identification and Application of Rheological Parameters of SurroundingRocks of Mountain Tunnels[J].Modern Tunnelling Technology,2009,46(5):61~65(in Chinese)
[11]陈子荫.围岩力学中的解析方法[M].北京:煤炭工业出版杜,1994Chen Ziyin.Analytic Methods in Surrounding Rock Mechanics[M].Beijing:China Coal Industry Publishing House,1994(in Chi-nese)
[12]吕爱钟,张路青.地下隧洞力学分析的复变函数方法[M].北京:科学出版社,2007Lu Aizhong,Zhang Luqing.Complex Function Method of Mechanical Analysis for Underground Tunnel[C].Beijing:SciencePress,2007(in Chinese)
[13]She Yuanguo,Chengwu Shen.Chaotic Search-based Adaptive Immune Genetic Algorithm.In:Shouyang Wang,Lean Yu,Fenghua Wen,Shaoyi He,Yong Fang,K.K.Lai,eds.,Proc.of the Second International Conference on Business Intelligence andFinancial Engineering[C].Beijing:IEEE Computer Society,2009,74~78
[2]S.Sakurai and K.Takeuchi.Back Analysis of Measured Displacement of Tunnel[J].Rock Mech.And Rock Eng.,1983,16(3):173~180
[3]吕爱钟.巷道围岩参数及地应力可辨识性的探讨[J].岩石力学与工程学报,1988,7(2):155~164Lu Aizhong.Discussion of Identifiability for Parameters of the Surrounding Rock of a Tunnel and in Situ Stress[J].Chinese Journalof Rock Mechanics and Engineering,1988,7(2):155~164(in Chinese)
[4]杨林德,朱合华,冯紫良,等.岩土工程问题的反演理论及工程实例[M].北京:科学出版社,1996Yang Linde,Zhu Hehua,Feng Ziliang,etc.al.Back Analysis Theory of Geotechnical Engineering Problems and Its EngineeringPractice[M].Beijing:Science Press,1996.(in Chinese)
[5]吕爱钟,蒋斌松.岩石力学反分析问题[M].北京:煤炭工业出版社,1998Lu Aizhong,Jiang Binsong.Back Analysis Issues of Rock Mechanics[M].Beijing:China Coal Industry Publishing House,1998(inChinese)
[6]张路青,贾正雪.弹性位移反分析对地应力、弹模的反演唯一性[J].岩土工程学报,2001,23(2):172~177Zhang Luqing,Jia ZhengXue.Inversion Uniqueness of Elastic Displacement Back-analysis for Ground Stress,Elastic Modulus andPoisson's Ratio[J].Chinese Journal of Geotechnical Engineering,2001,23(2):172~177(in Chinese)
[7]杨志法,王思敬,冯紫良,等.岩土工程反分析原理及应用[M].北京:地震出版社,2003Yang Zhifa,Wang Sijing,Feng Ziliang,etc.al.Principle and Application of Back-analysis in Geotechical Engineering[M].Bei-jing:Earthquake Press,2003(in Chinese)
[8]王登刚,刘迎曦,李守巨,等.巷道围岩初始应力场和弹性模量的区间反演方法[J].岩石力学与工程学报,2002,21(3):305~308Wang Denggang,Liu Yingxi,Li Shouju,etc.al.Interval Back Analysis on Initial Stresses and Elastic Modulus of SurroundingRocks of Tunnels[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(3):305~308(in Chinese)
[9]吴祥松,朱合华,叶飞.岩土工程参数反分析的可辨识性研究[J].地下空间与工程学报,2006,2(3):377~379Wu Xiangsong,Zhu Hehua,Ye Fei.Research on Identifiability of the Parameter in the Back Analysis of Geotechnical EngineeringProblems[J].Chinese Journal of Underground Space and Engineering,2006,2(3):377~379(in Chinese))
[10]袁鸿鹄,李云鹏,唐明明,等.山岭隧道围岩流变参数识别及应用研究[J].现代隧道技术,2009,46(5):61~65Yuan Honghu,Li Yunpeng,Tang Mingming,etc al.Identification and Application of Rheological Parameters of SurroundingRocks of Mountain Tunnels[J].Modern Tunnelling Technology,2009,46(5):61~65(in Chinese)
[11]陈子荫.围岩力学中的解析方法[M].北京:煤炭工业出版杜,1994Chen Ziyin.Analytic Methods in Surrounding Rock Mechanics[M].Beijing:China Coal Industry Publishing House,1994(in Chi-nese)
[12]吕爱钟,张路青.地下隧洞力学分析的复变函数方法[M].北京:科学出版社,2007Lu Aizhong,Zhang Luqing.Complex Function Method of Mechanical Analysis for Underground Tunnel[C].Beijing:SciencePress,2007(in Chinese)
[13]She Yuanguo,Chengwu Shen.Chaotic Search-based Adaptive Immune Genetic Algorithm.In:Shouyang Wang,Lean Yu,Fenghua Wen,Shaoyi He,Yong Fang,K.K.Lai,eds.,Proc.of the Second International Conference on Business Intelligence andFinancial Engineering[C].Beijing:IEEE Computer Society,2009,74~78
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