上覆分数导数粘弹性场地土地震放大效应
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摘要
基于一维波动模型和分数导数粘弹性本构关系,分析了在竖直方向上传播的剪切地震波作用下,基岩上分数导数粘弹性模型描述的场地土的横向振动问题,用直接刚度矩阵法求得了场地土的地震放大效应系数,并用数值算例讨论了相关参量对分数导数粘弹性场地土地震放大效应系数的影响。研究结果表明:在简谐剪切地震波作用下,分数导数粘弹性场地土存在共振现象;分数导数的阶数、模型参数和基岩与上覆场地土层底部之间的阻抗比对场地土的地震放大效应系数有较大的影响。
On a bedrock subjected to the steady state and vertically propagating shear seismic waves,the lateral vibration of the ground soil is investigated with one-dimensiona1 wave model and fractional derivative viscoelastic constitutive,the amplification factor is obtained based on the method of direct stiffness matrix,the influences of related parameters on the seismic amplification factor is analyzed by a numerical example.The result indicates that the ground soil described by fractional derivative viscoelastic model has a resonance under the excitation of steady state shear seismic waves,and the order of fractional derivative,model parameter and impedance ratio have big effects on the seismic amplification factor of ground soil.
On a bedrock subjected to the steady state and vertically propagating shear seismic waves,the lateral vibration of the ground soil is investigated with one-dimensiona1 wave model and fractional derivative viscoelastic constitutive,the amplification factor is obtained based on the method of direct stiffness matrix,the influences of related parameters on the seismic amplification factor is analyzed by a numerical example.The result indicates that the ground soil described by fractional derivative viscoelastic model has a resonance under the excitation of steady state shear seismic waves,and the order of fractional derivative,model parameter and impedance ratio have big effects on the seismic amplification factor of ground soil.
引文
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[2]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):1003-1031.
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[4]高玉峰.成层地基一维土层地震反应解析解[J].岩土工程学报,1999,21(4):498-500.
[5]栾茂田,刘占阁.成层场地振动特性及地震反应简化解析解的完整形式[J].岩土工程学报,2003,25(6):747-749.
[6]尚守平,李刚,任慧.剪切模量沿深度按指数规律增大的场地土的地震放大效应[J].工程力学,2005,22(5):155-157.
[7]刘林超,杨骁.竖向集中力作用下分数导数型半无限体粘弹性地基变形分析[J].工程力学,2009,26(1):13-17.
[8]Drozdov A,Kalamkarov A L.Constitutive model for nonlinear viscoelastic behavior of polymer[J].Polymer Engrg&Sci,1996,36(14):1907-1919.
[9]刘林超,张卫.具有分数Kelvin模型的粘弹性岩体中水平圆形硐室的变形特性[J].岩土力学,2005,26(2):287-289.
[10]Miller K S,Ross B.An introduction to the fractional calculus and fractional differential equations[M].New York:Wiley,1993.
[11]Podlubny I.Fractional differential equation:An introduction to fractional derivatives,fractional differential equations,some methods of their solution and some of their applications[M].Academic Press,San Diego,1999.
[2]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):1003-1031.
[3]Davis R.Effects of weathering on site response[J].Earthquake Engineering and Structure Dynamics,1995,24(2):301-309.
[4]高玉峰.成层地基一维土层地震反应解析解[J].岩土工程学报,1999,21(4):498-500.
[5]栾茂田,刘占阁.成层场地振动特性及地震反应简化解析解的完整形式[J].岩土工程学报,2003,25(6):747-749.
[6]尚守平,李刚,任慧.剪切模量沿深度按指数规律增大的场地土的地震放大效应[J].工程力学,2005,22(5):155-157.
[7]刘林超,杨骁.竖向集中力作用下分数导数型半无限体粘弹性地基变形分析[J].工程力学,2009,26(1):13-17.
[8]Drozdov A,Kalamkarov A L.Constitutive model for nonlinear viscoelastic behavior of polymer[J].Polymer Engrg&Sci,1996,36(14):1907-1919.
[9]刘林超,张卫.具有分数Kelvin模型的粘弹性岩体中水平圆形硐室的变形特性[J].岩土力学,2005,26(2):287-289.
[10]Miller K S,Ross B.An introduction to the fractional calculus and fractional differential equations[M].New York:Wiley,1993.
[11]Podlubny I.Fractional differential equation:An introduction to fractional derivatives,fractional differential equations,some methods of their solution and some of their applications[M].Academic Press,San Diego,1999.
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