基于双曲正切函数的土动力非线性本构模型
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摘要
基于双曲正切函数,构造了一种新的土动力非线性本构模型。该模型从双曲正切函数出发,通过平移和缩放构造了土动力应力应变关系的骨架曲线和卸载、反向加载的滞回曲线。相对于其他模型而言,这种新的数学模型参数较少,物理概念明确,形式简单,更利于编程实现,加卸载应力应变关系曲线只需要记忆加卸载转折点处的应力和应变值。将该数学模型应用于场地地震反应分析中,并与常用的等效线性化方法的地震反应结果进行比较,结果初步证明了该本构模型的可行性。
A new nonlinear soil constitutive model based on hyperbolic tangent function is presented,in which the shape of proposed backbone curve is the same as that of the hyperbolic tangent function curve shifted and enlarged by two factors.Such new model is expressed in a simple form and has a straightforward physical meaning.It can be executed by the computer without large computer memory.The only thing needs to be done for obtaining hysteresis loop is the determination of original shear strain and shear stress values at the beginning of unloading and reloading.Efforts have also been made in the seismic ground response analysis with a program developed based on this new stress-strain model.Results comparison with that carried out by the equivalent linear method shows that it is feasible to use this new constitutive model in seismic ground response analysis.Practical significance is of interest to develop such nonlinear soil constitutive model.
A new nonlinear soil constitutive model based on hyperbolic tangent function is presented,in which the shape of proposed backbone curve is the same as that of the hyperbolic tangent function curve shifted and enlarged by two factors.Such new model is expressed in a simple form and has a straightforward physical meaning.It can be executed by the computer without large computer memory.The only thing needs to be done for obtaining hysteresis loop is the determination of original shear strain and shear stress values at the beginning of unloading and reloading.Efforts have also been made in the seismic ground response analysis with a program developed based on this new stress-strain model.Results comparison with that carried out by the equivalent linear method shows that it is feasible to use this new constitutive model in seismic ground response analysis.Practical significance is of interest to develop such nonlinear soil constitutive model.
引文
[1]Masing G.Eigenspannungeu und verfertigung beim Messing[C]∥Proceedings of the 2nd International Congress on Applied Mechanics Zurich,1926.
[2]Rosenblueth E,Herrear I.On a kind of hysteretic damping[J].Journal of the Engineering Mechanics Division,ASCE,1964,90(4):37-47.
[3]张克绪,谢君斐.土动力学[M].北京:地震出版社.1989.
[4]Newmark N M,Rosenbluth E A.Fundamentals of earthquake engineering[M].Prentice Hall Inc.,Englewood Cliffs,N.J.,1971:163-19.
[5]Pyke R.Nonlinear soil models for irregular cyclic loadings[J].Journal of Geotechnical Engineering Division,American Society of Civil Engi-neers,1979,105(GJ6):715-726.
[6]Martin P P.Nonlinear method for dynamic analysis of ground response[D].Ph.D.Thesis,University of California,Berkeley,1975.
[7]Martin P P,Seed HB.One dimensional dynamic ground response analysis[J].Journal of Geotechnical Engineering,ASCE,1982,108(7):935-954.
[8]陈国兴,庄海洋.基于Davidenkov骨架曲线的土体动力本构关系及其参数研究[J].岩土工程学报,2005,27(8):860-864.
[2]Rosenblueth E,Herrear I.On a kind of hysteretic damping[J].Journal of the Engineering Mechanics Division,ASCE,1964,90(4):37-47.
[3]张克绪,谢君斐.土动力学[M].北京:地震出版社.1989.
[4]Newmark N M,Rosenbluth E A.Fundamentals of earthquake engineering[M].Prentice Hall Inc.,Englewood Cliffs,N.J.,1971:163-19.
[5]Pyke R.Nonlinear soil models for irregular cyclic loadings[J].Journal of Geotechnical Engineering Division,American Society of Civil Engi-neers,1979,105(GJ6):715-726.
[6]Martin P P.Nonlinear method for dynamic analysis of ground response[D].Ph.D.Thesis,University of California,Berkeley,1975.
[7]Martin P P,Seed HB.One dimensional dynamic ground response analysis[J].Journal of Geotechnical Engineering,ASCE,1982,108(7):935-954.
[8]陈国兴,庄海洋.基于Davidenkov骨架曲线的土体动力本构关系及其参数研究[J].岩土工程学报,2005,27(8):860-864.
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