基于达维坚科夫骨架曲线的软土非线性动力本构模型研究
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摘要
试验研究表明,上海地区软土的动力变形特性符合"应变软化"规律,可用达维坚科夫(Давидеков)模型描述。首先以达维坚科夫骨架曲线为基础,采用Masing法则,构造了土体加载、再卸载的动应力-应变关系滞回曲线,推导了达维坚科夫骨架曲线和卸载、再加载滞回曲线的增量剪切模量表达式。随后将土体动应力-应变关系曲线从一维推广到三维应变空间,基于FLAC3D提供的二次开发平台,编制了基于达维坚科夫骨架曲线和符合广义Masing法则的土体非线性动力本构模型计算程序,并且通过复杂加载路径验证了编制程序的正确性和合理性。以相关文献中的土体动剪切模量比maxG/G随剪应变幅值变化,以及阻尼比D随剪应变幅值变化的试验结果为依据,运用编制程序计算了不同剪应变幅值下的maxG/G-和D-曲线,并与文献试验结果进行了对比。研究结果表明,相比于工程上广泛应用的Hardin-Drnevich模型,基于达维坚科夫骨架曲线构造的本构模型所得到的软土maxG/G-和D-曲线能与试验结果更符合,进而验证了所建立的本构模型的合理性与实用性,其结果可用于上海地区软土场地的动力计算反应分析。
Test data show that dynamic deformation characteristics of Shanghai soft soils are consistent with law of strain softening;and they can be described by Davidenkov model well.Firstly,based on Davidenkov skeleton curve,the dynamic shear stress-strain curves for loading and unloading are constituted by Masing rules;and the equations of incremental tangent shear modulus of skeleton curve and hysteresis curves are derived.Then the dynamic stress-strain relation is extended from one-dimensional to three-dimensional strain space.Using the development platform of FLAC3D,the nonlinear dynamic model of soils is programmed,which is based on Davidenkov skeleton curve and according with generalized Masing rules;and the validity and rationality of the program are validated by a complex stress-strain loading path.Finally,based on the soft soils test data of other related study,the calculated results by the program and test data results of related study,which contain the relation curves of dynamic shear modulus ratio vs.shear strain amplitude and damping ratio D vs.shear strain amplitude,are compared under series of different levels of shear strain amplitude.Study results show that compared with Hardin-Drnevich model which is widely used in engineering,the-curves and D-curves based on the Davidenkov skeleton curve are fitting to the soft soils test results better,so as to prove the rationality and practicability of the proposed constitutive model,and can be used for the dynamic response analysis of soft soils sites in Shanghai.
Test data show that dynamic deformation characteristics of Shanghai soft soils are consistent with law of strain softening;and they can be described by Davidenkov model well.Firstly,based on Davidenkov skeleton curve,the dynamic shear stress-strain curves for loading and unloading are constituted by Masing rules;and the equations of incremental tangent shear modulus of skeleton curve and hysteresis curves are derived.Then the dynamic stress-strain relation is extended from one-dimensional to three-dimensional strain space.Using the development platform of FLAC3D,the nonlinear dynamic model of soils is programmed,which is based on Davidenkov skeleton curve and according with generalized Masing rules;and the validity and rationality of the program are validated by a complex stress-strain loading path.Finally,based on the soft soils test data of other related study,the calculated results by the program and test data results of related study,which contain the relation curves of dynamic shear modulus ratio vs.shear strain amplitude and damping ratio D vs.shear strain amplitude,are compared under series of different levels of shear strain amplitude.Study results show that compared with Hardin-Drnevich model which is widely used in engineering,the-curves and D-curves based on the Davidenkov skeleton curve are fitting to the soft soils test results better,so as to prove the rationality and practicability of the proposed constitutive model,and can be used for the dynamic response analysis of soft soils sites in Shanghai.
引文
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[17]CAMILO PHILLIPS,YOUSSEF M A.HASHASH.Damping formulation for nonlinear 1D site responseanalyses[J].Soil Dynamics and Earthquake Engi-neering,2009,29(7):1143-1158.
[2]齐文浩,薄景山.土层地震反应等效线性化方法综述[J].世界地震工程,2007,23(4):221-226.QI Wen-hao,BO Jing-shan.Summarization on equivalentlinear method of seismic responses for soil layers[J].World Earthquake Engineering,2007,23(4):221-226.
[3]WANG Z L,DAFALIAS Y F,SHEN C K.Boundingsurface hypoplasticity model for sand[J].Journal ofEngineering Mechanics,ASCE,1990,116(5):983-1001.
[4]HARDIN B O,RICHART F E.Elastic wave velocities ingranular soils[J].Journal of the Soil Mechanics andFoundations Division,ASCE,1963,89(SM1):33-65.
[5]HARDIN B O,DRNEVICH V P.Shear modulus anddamping in soil:design equations and curves[J].Journalof the Soil Mechanics and Foundation EngineeringDivision,ASCE,1972,98(7):667-692.
[6]MARTIN P P,SEED H B.One dimensional dynamicground response analysis[J].Journal of GeotechnicalEngineering,ASCE,1982,108(7):935-954.
[7]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.CHEN Guo-xing,ZHUANG Hai-yang.Developednonlinear dynamic constitutive relations of soils based onDavidenkov skeleton curve[J].Chinese Journal ofGeotechnical Engineering,2005,27(8):860-864.
[8]杨林德,陆忠良,白延辉,等.上海地铁车站抗震设计方法研究[R].上海:同济大学防灾救灾研究所,2002.
[9]刘齐建.软土地铁建筑结构抗震设计计算理论的研究[博士学位论文D].上海:同济大学,2005.
[10]MASING G.Eigenspannungen und Verfestingung beimMessing[C]//Proceedings of the 2nd International Con-gress of Applied Mechanics.Zurich:[s.n.],1926:332-335.
[11]陈育民,刘汉龙.邓肯-张本构模型在FLAC3D中的开发与实现[J].岩土力学,2007,28(10):2123-2126.CHEN Yu-min,LIU Han-long.Development andimplementation of Duncan-Chang constitutive model inFLAC3D[J].Rock and Soil Mechanics,2007,28(10):2123-2126.
[12]CUNDALL P A.A simple hysteretic damping formulationfor dynamic continuum simulations[C]//Proceedings ofthe 4th International FLAC Symposium on NumericalModeling in Geomechanics.Minneapolis:Itasca Con-sulting Group,2006.
[13]ROSENBLUETH E,HERREAR I.On a kind ofhysteretic damping[J].Journal of the EngineeringMechanics Division,ASCE,1964,90(4):37-47.
[14]NEWMARK N M,ROSENBLUTH E A.Fundamentalsof earthquake engineering[M].Englewood Cliffs:PrenticeHall Inc.,1971:163-192.
[15]朱战立.数据结构(C++语言描述)[M].北京:高等教育出版社,2004.
[16]IDRISS I M,SUN J I.User's Manual for Shake91 Centerfor Geotechnical Modeling[D].Davis:Department ofCivil&Environmental Engineering,University ofCalifornia,1992.
[17]CAMILO PHILLIPS,YOUSSEF M A.HASHASH.Damping formulation for nonlinear 1D site responseanalyses[J].Soil Dynamics and Earthquake Engi-neering,2009,29(7):1143-1158.
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