地下结构抗震分析中若干土层模拟方法对比研究
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摘要
动力时程在地下结构抗震分析中应用广泛,土体动力特性的准确模拟对动力时程分析结果有重要影响。介绍了Rayleigh阻尼和Hardin-Drnevich模型的基本理论,验证了等位移边界条件的有效性。从地表加速度响应和加速度幅值沿深度放大两方面,对比分析Mohr coulomb模型、Shake91、Rayleigh阻尼和Hardin-Drnevich模型在2Hz和8Hz正弦波作用下的响应结果。结合理论分析得出:静力Mohr coulomb模型对动力时程分析适用性有限;建议在地下结构抗震分析中采用场地基频与接近地震波主频固有频率计算Rayleigh阻尼参数;Hardin-Drnevich等粘弹性非线性模型比等效线性化方法更适用于地下结构抗震分析。
Time history analysis is widely applied in seismic analysis of underground structures,and the simulation of soil ground under dynamic loads has a significant influence on the result.Formulations of Rayleigh damping and Hardin-Drnevich model are introduced in the paper.The repeatable boundary condition is validated through comparison with far free boundary.On the basis of the repeatable boundary condition,the numerical simulation results with Shake91 model,Rayleigh damping model,Mohr coulomb model and Hardin-Drnevich model under 2 Hz and 8 Hz sine waves are compared from two aspects,that is,the ground surface acceleration responses and the peak acceleration profiles along depth.It is concluded that the Mohr coulomb model has limited applicability in dynamic time history analysis due to its constitutive model theory.It is recommended that the Rayleigh damping parameters be calculated with the fundamental frequency of soil ground and the natural frequency that approaching the dominant frequency of the imposed seismic wave.The viscoelastic model(e.g.Hardin-Drnevich model)is more suitable for seismic analysis of underground structures than the equivalent linear method,namely Shake91 model and Rayleigh damping model.
Time history analysis is widely applied in seismic analysis of underground structures,and the simulation of soil ground under dynamic loads has a significant influence on the result.Formulations of Rayleigh damping and Hardin-Drnevich model are introduced in the paper.The repeatable boundary condition is validated through comparison with far free boundary.On the basis of the repeatable boundary condition,the numerical simulation results with Shake91 model,Rayleigh damping model,Mohr coulomb model and Hardin-Drnevich model under 2 Hz and 8 Hz sine waves are compared from two aspects,that is,the ground surface acceleration responses and the peak acceleration profiles along depth.It is concluded that the Mohr coulomb model has limited applicability in dynamic time history analysis due to its constitutive model theory.It is recommended that the Rayleigh damping parameters be calculated with the fundamental frequency of soil ground and the natural frequency that approaching the dominant frequency of the imposed seismic wave.The viscoelastic model(e.g.Hardin-Drnevich model)is more suitable for seismic analysis of underground structures than the equivalent linear method,namely Shake91 model and Rayleigh damping model.
引文
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[2]城市轨道交通结构抗震设计规范:GB50909-2014[S].北京:中国计划出版社,2014.Code for seismic design of urban rail transit:GB50909-2014[S].Beijing:China Planning Press,2014.(in Chinese)
[3]Huo H,Bobet A,Fernández G,et al.Load transfer mechanisms between underground structure and surrounding ground:evaluation of the failure of the daikai station[J].Journal of Geotechnical and Geoenvironmental Engineering,2005,131(12):1 522-1 533.
[4]Yu H,Yuan Y,Qiao Z,et al.Seismic analysis of a long tunnel based on multi-scale method[J].Engineering Structures,2013,49:572-587.
[5]Wang J N.Seismic design of tunnels:a simple stateof-the-art design approach[M].New York:Parsons Brinckerhoff Inc,1993.
[6]Elgamal A,Yang Z,Parra E,et al.Modeling of cyclic mobility in saturated cohesionless soils[J].International Journal of Plasticity,2003,19(6):883-905.
[7]Zhang F,Ye B,Noda T,et al.Explanation of cyclic mobility of soils:approach by stress-induced anisotropy[J].Soils&Foundations,2007,47(4):635-648.
[8]Dafalias Y F,Manzari M T.Simple plasticity sand model accounting for fabric change effects[J].Journal of Engineering Mechanics,2004,130(6):622-634.
[9]Hardin B O,Dmevich V P.Shear modulus and damping in soils:design equation and curves[J].Journal of the Soil Mechanics&Foundations Division,1972,98:667-692.
[10]邬洋.框架式地下建筑结构抗震性能分析[D].重庆:重庆大学,2012.Wu Y.Analysis on seismic performance of frame-type underground construction[D].Chongqing:Chongqing University,2012.(in Chinese)
[11]Amorosi A,Boldini D,Elia G.Parametric study on seismic ground response by finite element modelling[J].Computers and Geotechnics,2010,37(4):515-528.
[12]ABAQUS Inc.ABAQUS User Manual.Version 6.10[M].Pawtucket US:ABAQUS Inc,2010.
[13]赵丁凤,阮滨,陈国兴,等.基于Davidenkov骨架曲线模型的修正不规则加卸载准则与等效剪应变算法及其验证[J].岩土工程学报,2017,39(5):888-895.Zhao D F,Ruan B,Chen G X,et al.Validation of modified irregular loading-unloading rules based on Davidenkov skeleton curve and its equivalent shear strain algorithm implemented in ABAQUS[J].Chinese Journal of Geotechnical Engineering,2017,39(5):888-895.(in Chinese)
[14]Zienkiewicz O C,Chan A H C,Pastor M,et al.Computational geomechanic with special Reference to Earthquake Engineering[M].Chichester:Wiley,1999.
[15]Kokusho T.Cyclic triaxial test on dynamic soil properties for wide strain range[J].Soils and Foundations,1980,20(2):45-60.
[16]庄海洋,陈国兴,梁艳仙,等.土体动非线性黏弹性模型及其ABAQUS软件的实现[J].岩土力学,2007,28(3):436-442.Zhuang H Y,Chen G X,Liang Y X,et al.A developed dynamic viscoelastic constitutive relations of soil and implemented by ABAQUS software[J].Rock and Soil Mechanics,2007,28(3):436-442.(in Chinese)
[17]Idriss I M,Seed H B.Seismic response of horizontal soil layers[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1968,94(4):1 003-1 031.
[18]楼梦麟,邵新刚.深覆盖土层Rayleigh阻尼矩阵建模问题的讨论[J].岩土工程学报,2013,35(7):1 272-1279.Lou M L,Shao X G.Discussion on modeling issues of Rayleigh damping matrix in soil layers with deep deposit[J].Chinese Journal of Geotechnical Engineering,2013,35(7):1 272-1 279.(in Chinese)
[19]胡聿贤.地震工程学[M].2版.北京:地震出版社,2006.Hu Y X.Earthquake engineering[M].2nd ed.Beijing:Seismological Press,2006.(in Chinese)