群桩基础引发饱和地基振动的近似解析解
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摘要
建立了饱和半空间-群桩基础耦合动力近似解析模型,其中基桩考虑为欧拉梁,饱和地基采用Biot两相介质动力控制方程,二者在频率-波数域中利用桩-土相互作用点处的饱和地基柔度矩阵进行耦合,并采用快速傅里叶逆变换获得频域解答。分析了饱和地基中群桩基础的动力阻抗及刚性承台上施加简谐振动荷载时群桩基础引起的饱和地基振动响应。研究结果表明,荷载类型、激振频率以及地基渗透系数对饱和地基位移和孔压响应有明显影响。特别的,群桩基础动力阻抗峰值频率会随着地基渗透系数的增加而增大。
An approximate analytical model has been established in this paper to study dynamic interactions between the saturated soil and the pile group with assumption of poroelastic half-space. The piles are modeled as Bernoulli-Euler elastic beams, and the saturated half-space is governed by Biot's dynamic equations. The pile beams and the saturated half-space are coupled through receptance matrix established at pile/soil interaction points in frequency-wavenumber domain. Results are obtained by fast Fourier transform. The dynamic impedances of the pile group have been analyzed. Meanwhile, the results demonstrated that the type and frequency of the excitation force and the soil permeability have significant influences on displacement and pore pressure responses of the saturated ground. Especially, it is noted that peak frequencies of pile-foundation impedance increase along with the increasing of soil permeability.
An approximate analytical model has been established in this paper to study dynamic interactions between the saturated soil and the pile group with assumption of poroelastic half-space. The piles are modeled as Bernoulli-Euler elastic beams, and the saturated half-space is governed by Biot's dynamic equations. The pile beams and the saturated half-space are coupled through receptance matrix established at pile/soil interaction points in frequency-wavenumber domain. Results are obtained by fast Fourier transform. The dynamic impedances of the pile group have been analyzed. Meanwhile, the results demonstrated that the type and frequency of the excitation force and the soil permeability have significant influences on displacement and pore pressure responses of the saturated ground. Especially, it is noted that peak frequencies of pile-foundation impedance increase along with the increasing of soil permeability.
引文
[1]史吏,曹志刚,潘晓东.温州市域铁路S1线一期工程对状元水厂振动影响评估及控制对策研究报告[R].杭州:浙江工业大学,2016.SHI Li,CAO Zhi-gang,PAN Xiao-dong.Research report on the vibration impact assessment and control strategy of the first phase project of Wenzhou municipal railway line S1[R].Hangzhou:Zhejiang University of Technology,2016.
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[5]WU G X,LIAM FINN W D.Dynamic elastic analysis of pile foundations using finite element method in frequency domain[J].Canadian Geotechnical Journal,1997,34:34-43.
[6]MAMOON S M,KAYNIA A M.Frequency domain dynamic analysis of piles and pile groups[J].Journal of Engineering Mechanics,1990,116(10):2238-2257.
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[9]王小岗.横观各向同性饱和层状土中垂直受荷群桩的动力阻抗[J].岩土工程学报,2011,33(11):1759-1766.WANG Xiao-gang.Dynamic impedance of groups subjected to vertical load in layered transversely isotropic saturated soils[J].Chinese Journal of Geotechnical Engineering,2011,33(11):1759-1766.
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[12]DOBRY R,GAZETAS G.Simple method for dynamic stiffness and damping of floating pile groups[J].Geotechnique,1988,38(4):557-574.
[13]刘林超,杨骁.饱和土中桩-桩竖向动力相互作用及群桩竖向振动[J].工程力学,2011,28(1):124-130.LIU Lin-chao,YANG Xiao.Pile to pike vertical dynamic interaction and vertical vibration of pile groups in saturated soil[J].Engineering Mechanics,2011,28(1):124-130.
[14]蒯行成,沈蒲生.层状介质中群桩竖向和摇摆动力阻抗的简化计算方法[J].土木工程学报,1999,32(5):62-70.KUAI Xing-cheng,SHEN Pu-sheng.A simple calculation method for vertical and swing dynamic impedances of pile groups in layered medium[J].China Civil Engineering Journal,1999,32(5):62-70.
[15]熊辉,江雅丰,禹荣霞.层状地基中基于Laplace变换的桩基横向振动阻抗计算[J].岩土力学,2018,39(5):1901-1907.XIONG Hui,JIANG Ya-feng,YU Rong-xia.Lateral vibration impedance of piles embedded in layered soil based on Laplace transform[J].Rock and Soil Mchanics,2018,39(5):1901-1907.
[16]KAYNIA A M,KAUSEL E.Dynamic of piles and pile groups in layered soil media[J].Soil Dynamic and Earthquake Engineering,1991,10(8):386-401.
[17]JIN B,LIU H.Dynamic response of a poroelastic half space to horizontal buried loading[J].International Journal of Solid and Structures,2001,38:8053-8064.
[18]NOGAMI T.Thin layer element method for dynamic soil-structure interaction analysis of axi-symmetric structure in submerger soil[J].Soil Dynamics and Earthquake Engineering,1997,16(5):337-351.
[19]王鹏,史吏,王军,等.三维层状地基动力Green函数的薄层法求解.岩土力学,2014,35(12):3602-3610.WANG Peng,SHI Li,WANG Jun,et al.Dynamic Green function solution of three-dimensional layered saturated ground using thin layer element method[J].Rock and Soil Mechanics,2014,35(12):3602-3610.
[20]SHI L,XU C J,CAI Y Q,et al.Dynamic impedances and free-field vibration analysis of pile groups in saturated ground[J].Journal of Sound and Vibration,2014,333:3709-3731.
[21]BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid I.low frequency range[J].Journal of the Acoustical Society of America,1965,28(2):179-191.
[22]DEGRANDE G,DE ROECK G.An absorbing boundary condition for propagation in saturated poroelastic media-Part I:formulation and efficiency evaluation[J].Soil Dynamics and Earthquake Engineering,1992,12(7):411-421.
[23]CHEN S L,CHEN L Z,PAN E.Three-dimensional time-harmonic Green’s functions of saturated soil under buried loading[J].Soil Dynamics and Earthquake Engineering,2007,27:448-462.
[2]RAJAPAKSE R K N D,SHAH A H.On the longitudinal harmonic motion of an elastic bar embedded in an elastic halfspace[J].International Journal of Solids and Structures,1987,23(2):357-285.
[3]PAK R Y S,JENNINGS P C.Elastodynamic response of pile under transverse excitations[J].Journal of Engineering Mechanics,1987,113(7):1101-1116.
[4]ZENG X,RAJAPAKSE R K N D.Dynamic axial load transfer from elastic bar to poroelastic medium[J].Journal of Engineering Mechanics,1999,125(9):1018-1055.
[5]WU G X,LIAM FINN W D.Dynamic elastic analysis of pile foundations using finite element method in frequency domain[J].Canadian Geotechnical Journal,1997,34:34-43.
[6]MAMOON S M,KAYNIA A M.Frequency domain dynamic analysis of piles and pile groups[J].Journal of Engineering Mechanics,1990,116(10):2238-2257.
[7]PADRON L A,AZNAREZ J J,MAESO O.Dynamic analysis of piled foundations in stratified soils by a BEM-FEM mode[J].Soil Dynamics and Earthquake Engineering,2008,28:333-346.
[8]MAESO O,AZNAREZ J J,GARCIA F.Dynamic impedance of piles and groups of piles in saturated soils[J].Computers&Structures,2005,83:769-782.
[9]王小岗.横观各向同性饱和层状土中垂直受荷群桩的动力阻抗[J].岩土工程学报,2011,33(11):1759-1766.WANG Xiao-gang.Dynamic impedance of groups subjected to vertical load in layered transversely isotropic saturated soils[J].Chinese Journal of Geotechnical Engineering,2011,33(11):1759-1766.
[10]高广运,何俊峰,高萌,等.分层土中群桩水平动力阻抗的改进计算[J].岩土力学,2010,31(2):509-515.GAO Guang-yun,HE Jun-feng,GAO Meng,et al.Improved calculation for lateral dynamic impedance of pile groups in layered soil[J].Rock and Soil Mchanics,2010,33(2):509-515.
[11]任青,黄茂松,钟锐,等.部分埋入群桩的竖向振动特性[J].岩土工程学报,2009,31(9):1384-1390.REN Qin,HUANG Mao-song,ZHONG Rui,et al.Vertical vibration of partially embedded pile groups[J].Chinese Journal of Geotechnical Engineering,2009,31(9):1384-1390.
[12]DOBRY R,GAZETAS G.Simple method for dynamic stiffness and damping of floating pile groups[J].Geotechnique,1988,38(4):557-574.
[13]刘林超,杨骁.饱和土中桩-桩竖向动力相互作用及群桩竖向振动[J].工程力学,2011,28(1):124-130.LIU Lin-chao,YANG Xiao.Pile to pike vertical dynamic interaction and vertical vibration of pile groups in saturated soil[J].Engineering Mechanics,2011,28(1):124-130.
[14]蒯行成,沈蒲生.层状介质中群桩竖向和摇摆动力阻抗的简化计算方法[J].土木工程学报,1999,32(5):62-70.KUAI Xing-cheng,SHEN Pu-sheng.A simple calculation method for vertical and swing dynamic impedances of pile groups in layered medium[J].China Civil Engineering Journal,1999,32(5):62-70.
[15]熊辉,江雅丰,禹荣霞.层状地基中基于Laplace变换的桩基横向振动阻抗计算[J].岩土力学,2018,39(5):1901-1907.XIONG Hui,JIANG Ya-feng,YU Rong-xia.Lateral vibration impedance of piles embedded in layered soil based on Laplace transform[J].Rock and Soil Mchanics,2018,39(5):1901-1907.
[16]KAYNIA A M,KAUSEL E.Dynamic of piles and pile groups in layered soil media[J].Soil Dynamic and Earthquake Engineering,1991,10(8):386-401.
[17]JIN B,LIU H.Dynamic response of a poroelastic half space to horizontal buried loading[J].International Journal of Solid and Structures,2001,38:8053-8064.
[18]NOGAMI T.Thin layer element method for dynamic soil-structure interaction analysis of axi-symmetric structure in submerger soil[J].Soil Dynamics and Earthquake Engineering,1997,16(5):337-351.
[19]王鹏,史吏,王军,等.三维层状地基动力Green函数的薄层法求解.岩土力学,2014,35(12):3602-3610.WANG Peng,SHI Li,WANG Jun,et al.Dynamic Green function solution of three-dimensional layered saturated ground using thin layer element method[J].Rock and Soil Mechanics,2014,35(12):3602-3610.
[20]SHI L,XU C J,CAI Y Q,et al.Dynamic impedances and free-field vibration analysis of pile groups in saturated ground[J].Journal of Sound and Vibration,2014,333:3709-3731.
[21]BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid I.low frequency range[J].Journal of the Acoustical Society of America,1965,28(2):179-191.
[22]DEGRANDE G,DE ROECK G.An absorbing boundary condition for propagation in saturated poroelastic media-Part I:formulation and efficiency evaluation[J].Soil Dynamics and Earthquake Engineering,1992,12(7):411-421.
[23]CHEN S L,CHEN L Z,PAN E.Three-dimensional time-harmonic Green’s functions of saturated soil under buried loading[J].Soil Dynamics and Earthquake Engineering,2007,27:448-462.