邓肯–张模型参数反演的不唯一性
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摘要
对邓肯–张模型的特点进行了分析,指出待反演的参数中若同时包含破坏比Rf、凝聚力c和内摩擦角?容易导致反演失败的原因在于反演结果不唯一所引起的数值奇异。证明了不唯一性源于参数Rf,c,?之间的一种特殊相关性,即,对于任一特定的应力状态,有无数种Rf,c,?组合可以保证Rf S(破坏比Rf与应力水平S的乘积)取值不变并获得相同的切线模量Et和切线泊松比νt,导致满足反演目标函数获得相同最小值的参数组合出现不唯一性。提供了相应的解决方法,即重新拟定反演参数或约束Rf,c,?中的某些参数,以确保模型参数的可辨识性。
The fact that the back analysis procedure simultaneously selecting failure ratio,cohesion,and frictional angle as objective parameters in Duncan-Chang hyperbolic constitutive model tends to fail is caused by numerical singularity because of non-uniqueness of the solution.The non-uniqueness arises from the co-relation of,,and,which means there are innumerable groups of,,and which can form the same(product of failure ratio and stress level) and produce the same tangent modulus and tangent Poisson ratio under specific stress condition and finally provide the same objective value in back analysis.Effective methods are given to ensure the identification of Duncan-Chang hyperbolic constitutive model during back analysis by means of parameter reconstruction and parameter constraint.
The fact that the back analysis procedure simultaneously selecting failure ratio,cohesion,and frictional angle as objective parameters in Duncan-Chang hyperbolic constitutive model tends to fail is caused by numerical singularity because of non-uniqueness of the solution.The non-uniqueness arises from the co-relation of,,and,which means there are innumerable groups of,,and which can form the same(product of failure ratio and stress level) and produce the same tangent modulus and tangent Poisson ratio under specific stress condition and finally provide the same objective value in back analysis.Effective methods are given to ensure the identification of Duncan-Chang hyperbolic constitutive model during back analysis by means of parameter reconstruction and parameter constraint.
引文
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[5]TANG Yu-Geng,GORDON Tung-Chin Kung.Application of nonlinear optimization technique to back analyses of deep excavation[J].Computers and Geotechnics,2009,36:276–290.
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[10]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,2002.(YANG Zhi-fa,WANG Si-jing,FENG Zi-liang,et al.Principle and application of back analysis in geotechnical engineering[M].Beijing:Earthquake Press,2002.(in Chinese))
[11]ROLF Mahnken,ERWIN Stein.A unified approach for parameter identification of inelastic material models in the frame of the finite element method[J].Computer Methods in Applied Mechanics and Engineering,1996,136:225–258.
[12]RECHEA C,LEVASSEUR S,FINNO R.Inverse analysis techniques for parameter identification in simulation of excavation support systems[J].Computers and Geotechnics,2008,35:331–345.
[13]STéPHANE Avril,MARC Bonnet,ANNE-SOPHIE Bretelle.Overview of identification methods of mechanical parameters based on full-field measurements[J].Experimental Mechanics,2008,48:381–402.
[14]ZENTAR R,HICHER P Y,MOULIN G.Identification of soil parameters by inverse analysis[J].Computers and Geotechnics,2001,28:129–144.
[15]MICHELE Calvello,RICHARD J.Finno.Selecting parameters to optimize in model calibration by inverse analysis[J].Computers and Geotechnics,2004,31:411–425.
[2]KONDNER R L.Hyperbolic stress-strain response:cohesive soils[J].Journal of the Soil Mechanics and Foundation ASCE,1963,89(SM1):115–143.
[3]谭昌明,徐日庆,龚晓南,土体双曲线本构模型的参数反演[J].浙江大学学报(工学版),2001,35(1):57–61.(TAN Chang-ming,XU Ri-qing,GONG Xiao-nan.Parameter back-analysis of hyperbolic constitutive model in soils[J].Journal of Zhejian University(Engineering Science),2001,35(1):57–61.(in Chinese))
[4]胡应德,叶枫,陈志坚.土体邓肯–张非线性弹性模型参数反演分析[J].土木工程学报,2004,37(2):54–57.(HU Ying-de,YE Feng,CHEN Zhi-jian.Back-performing analysis for parameters of DUNCAN-CHANG nonlinear-elastic model[J].China Civil Engineering Journal,2004,37(2):54–57.(in Chinese))
[5]TANG Yu-Geng,GORDON Tung-Chin Kung.Application of nonlinear optimization technique to back analyses of deep excavation[J].Computers and Geotechnics,2009,36:276–290.
[6]GIODA G,MAIER G.Direct search solution of an inverse problem in elastoplasticity:identification of cohesion,friction angle and in situ stress by pressure tunnel tests[J].International Journal for Numerical Methods in Engineering,1980,15(12):1823–1848.
[7]SAKURAI S,TAKEUCHI K.Back analysis of measured displacements of tunnels[J].Rock Mechanics and Rock Engineering,1983,16:173–180.
[8]杨林德.岩土工程问题的反演理论与工程实践[M].北京:科学出版社,1996.(YANG Lin-de.Theory and practice of back analysis in geotechnical engineering[M].Beijing:Science Press,1996.(in Chinese))
[9]王芝银,杨志法,王思敬.岩石力学位移反演分析回顾及进展[J].力学进展,1998,28(4):488–498.(WANG Zhi-yin,YANG Zhi-fa,WANG Si-jing.A review on inverse analysis of displacements in rock mechanics[J].Advances in Mechanics,1998,28(4):488–498.(in Chinese))
[10]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,2002.(YANG Zhi-fa,WANG Si-jing,FENG Zi-liang,et al.Principle and application of back analysis in geotechnical engineering[M].Beijing:Earthquake Press,2002.(in Chinese))
[11]ROLF Mahnken,ERWIN Stein.A unified approach for parameter identification of inelastic material models in the frame of the finite element method[J].Computer Methods in Applied Mechanics and Engineering,1996,136:225–258.
[12]RECHEA C,LEVASSEUR S,FINNO R.Inverse analysis techniques for parameter identification in simulation of excavation support systems[J].Computers and Geotechnics,2008,35:331–345.
[13]STéPHANE Avril,MARC Bonnet,ANNE-SOPHIE Bretelle.Overview of identification methods of mechanical parameters based on full-field measurements[J].Experimental Mechanics,2008,48:381–402.
[14]ZENTAR R,HICHER P Y,MOULIN G.Identification of soil parameters by inverse analysis[J].Computers and Geotechnics,2001,28:129–144.
[15]MICHELE Calvello,RICHARD J.Finno.Selecting parameters to optimize in model calibration by inverse analysis[J].Computers and Geotechnics,2004,31:411–425.
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