考虑桩底土层波动效应的饱和黏弹性半空间中摩擦桩竖向振动
|
摘要
为深化对饱和黏弹性半空间地基中摩擦桩竖向振动特性的认识,基于Boer多孔介质动力控制方程组,考虑桩底土层波动效应,采用Hankel积分变换和微分算子分解理论求解相关方程得到桩底、桩侧反力,进而建立饱和土中桩基竖向振动偏微分方程,结合桩土接触面混合边值条件推导得出了饱和黏弹性半空间地基中摩擦桩桩顶竖向动力阻抗解析表达式。并在此基础上进一步通过数值算例对比分析探讨了液固耦合系数、桩长径比、桩土模量比、地基土黏滞阻尼系数这些重要因素对所得桩顶动力阻抗的影响规律,得到了一些对工程实践有意义的结论。
Considering the waves effect of soil under pile bottom, an axisymmetrical analytical solution is presented to investigate the vertical vibration of a floating pile embedded in a saturated viscoelastic half-space. By employing the Hankel's integral transformation and the decomposition theory of differential operator and considering the mixed boundary condition of pile-soil interfaces to solve the Boer's dynamic governing equations for the soil, the dynamic impedance of the pile head is obtained. Furthermore, the effects of liquid-solid coupled coefficient, length-radius ratio of piles, modulus ratio of pile-soil and viscous damping coefficient of soil on the obtained impedance are discussed through parametric comparative analyses. Some significant conclusions are drawn. This study may provide technical reference and theoretical support for the related engineering practices to some extent.
Considering the waves effect of soil under pile bottom, an axisymmetrical analytical solution is presented to investigate the vertical vibration of a floating pile embedded in a saturated viscoelastic half-space. By employing the Hankel's integral transformation and the decomposition theory of differential operator and considering the mixed boundary condition of pile-soil interfaces to solve the Boer's dynamic governing equations for the soil, the dynamic impedance of the pile head is obtained. Furthermore, the effects of liquid-solid coupled coefficient, length-radius ratio of piles, modulus ratio of pile-soil and viscous damping coefficient of soil on the obtained impedance are discussed through parametric comparative analyses. Some significant conclusions are drawn. This study may provide technical reference and theoretical support for the related engineering practices to some extent.
引文
[1]JIN B,ZHOU D,ZHONG Z.Lateral dynamic compliance of pile embedded in poroelastic half space[J].Soil Dynamics and Earthquake Engineering,2001,21:519–525.
[2]LU J F,JENG D S,NIE W D.Dynamic response of a pile embedded in a porous medium subjected to plane SH waves[J].Computers and Geotechnics,2006,33:404–418.
[3]CHEN G,CAI Y Q,LIU F Y,et al.Dynamic response of a pile in a transversely isotropic saturated soil to transient tensional loading[J].Computers and Geotechnics,2007,34(8):1–5.
[4]陆建飞.频域内半空间饱和土中水平受荷桩的动力分析[J].岩石力学与工程学报,2002,21(4):577–581.(LU Jian-fei.Dynamic frequency domain analysis on laterally loaded pile in saturated soil[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(4):577–581.(in Chinese))
[5]陆建飞,聂卫东.饱和土中单桩在瑞利波作用下的动力响应[J].岩土工程学报,2008,30(2):225–231.(LU Jian-fei,NIE Wei-dong.Dynamic response of single pile embedded in half-space saturated soil subjected to Rayleigh waves[J].Chinese Journal of Geotechnical Engineering,2008,30(2):225–231.(in Chinese))
[6]杨军,宋二祥,陈肇元.桩在饱和土中水平振动的辐射阻尼简化算法[J].岩土力学,2002,23(2):179–183.(YANG Jun,SONG Er-xiang,CHEN Zhao-yuan.Simple radiation damping model for horizontally vibrating pile in saturated soil[J].Rock and Soil Mechanics,2002,23(2):179–183.(in Chinese))
[7]张智卿,王奎华,谢康和.饱和土层中桩的扭转振动响应分析[J].浙江大学学报,2006,40(7):1211–1218.(ZHANG Zhi-qing,WANG Kui-hua,XIE Kang-he.Study on torsional vibration of pile embedded in saturated soil[J].Journal of Zhejiang University,2006,40(7):1211–1218.(in Chinese))
[8]李强,王奎华,谢康和.饱和土中端承桩纵向振动特性研究[J].力学学报,2004,36(4):435–442.(LI Qiang,WANG Kui-hua,XIE Kang-he.Vertical vibration of an end bearing pile embedded in saturated soil[J].Acta Mechanica Sinica,2004,36(4):435–442.(in Chinese))
[9]李强,王奎华,谢康和.饱和土中大直径嵌岩桩纵向振动特性研究[J].振动工程学报,2005,18(4):500–505.(LI Qiang,WANG Kui-hua,XIE Kang-he.Dynamic response for vertical vibration of large diameter pile in saturated soil[J].Journal of Vibration Engineering,2005,18(4):500–505.(in Chinese))
[10]李强.饱和土中端承桩非完全黏结下的竖向振动特性[J].水利学报,2007,38(3):349–354.(LI Qiang.Vertical vibration of piles embedded in saturated soil considering the imperfect contact[J].Journal of Hydraulic Engineering,2007,38(3):349–354.(in Chinese))
[11]尚守平,余俊,王海东,等.饱和土中桩水平振动分析[J].岩土工程学报,2007,29(11):1696–1702.(SHANG Shou-ping,YU Jun,WANG Hai-dong,et al.Horizontal vibration of piles in saturated soil[J].Chinese Journal of Geotechnical Engineering,2007,29(11):1696–1702.(in Chinese))
[12]刘林超,杨骁.基于多孔介质理论的饱和土-桩纵向耦合振动研究[J].土木工程学报,2009,42(9):89–95.(LIU Lin-chao,YANG Xiao.Study of vertical coupled vibrations of piles in saturated soils using porous medium theory[J].China Civil Engineering Journal,2009,42(9):89–95.(in Chinese))
[13]刘林超,苏子平.层状饱和土中单桩纵向振动分析[J].公路交通科技,2010,27(12):5–9.(LIU Lin-chao,SU Zi-ping.Analysis of vertical vibration of single pile in layered saturated soil[J].Journal of Highway and Transportation Research and Development,2010,27(12):5–9.(in Chinese))
[14]刘林超,闫启方.饱和土中管桩的纵向振动特性[J].水力学报,2011,42(3):366–378.(LIU Lin-chao,YAN Qi-fang.Vertical vibration characteristics of pipe pile in saturated soil[J].Journal of Hydraulic Engineering,2011,42(3):366–378.(in Chinese))
[15]杨骁,唐洁.成层饱和土中考虑横向惯性的单桩纵向振动[J].岩土力学,2013,34(6):1560–1566.(YANG Xiao,TANG Jie.Vertical vibration of single pile with transversal inertia effect in stratified saturated soil[J].Rock and Soil Mechanics,2013,34(6):1560–1566.(in Chinese))
[16]杨骁,刘慧,蔡雪琼.端承黏弹性桩纵向振动的轴对称解析解[J].固体力学学报,2012,33(4):423–430.(YANG Xiao,LIU Hui,CAI Xue-qiong.Axisymmetrical analytical solution for vertical vibration of end-bearing viscoelastic pile[J].Chinese Journal of Solid Mechanics,2012,33(4):423–430.(in Chinese))
[17]杨骁,蔡雪琼.考虑横向效应饱和黏弹性土层中桩的纵向振动[J].岩土力学,2011,32(6):1857–1863.(YANG Xiao,CAI Xue-qiong.Vertical vibration of pile in saturated viscoelastic soil layer considering transversal effects[J].Rock and Soil Mechanics,2011,32(6):1857–1863.(in Chinese))
[18]王小岗.横观各向同性饱和土中柱面载荷的动力Green函数[J].力学学报,2010,42(5):909–918.(WANG Xiao-gang.Dynamic Green’s function for internal barrel loads in transversely isotropic saturated soils[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(5):909–918.(in Chinese))
[19]闫启方,刘林超.基于多孔介质理论的饱和土中单桩的扭转复刚度研究[J].岩土工程学报,2010,32(9):1460–1463.(YAN Qi-fang,LIU Lin-chao.Torsional complex stiffness of single pile in saturated soil based on theory of porous medium[J].Chinese Journal of Geotechnical Engineering,2010,32(9):1460–1463.(in Chinese))
[20]闫启方,刘林超.考虑波动效应的SH简谐地震波作用下单桩水平振动研究[J].岩土工程学报,2012,34(8):1483–1487.(YAN Qi-fang,LIU Lin-chao.Lateral vibration of a single pile under SH harmonic seismic waves considering three-dimensional wave effect[J].Chinese Journal of Geotechnical Engineering,2012,34(8):1483–1487.(in Chinese))
[21]秦世伟,莫泷,史蕙质.轴力作用下液化土中端承桩的水平振动特性[J].岩土力学,2013,34(4):987–995.(QIN Shi-wei,MO Long,SHI Hui-zhi.Characteristics of horizontal vibration of end-bearing piles in liquefied soils under axial force[J].Rock and Soil Mechanics,2013,34(4):987–995.(in Chinese))
[22]王建华,陆建飞,王卫东,等.移动荷载作用下饱和土中单桩的动力响应[J].岩土力学,2007,28:693–697.(WANG Jian-hua,LU Jian-fei,WANG Wei-dong,et al.Dynamic response of a single pile embedded in a poroelastic soil to moving loads[J].Rock and Soil Mechanics,2007,28:693–697.(in Chinese))
[23]王国才,丁翠红,王哲,等.层状地基中单桩扭转振动特性分析[J].计算力学学报,2009,26(5):715–721.(WANG Guo-cai,DING Cui-hong,WANG Zhe,et al.Study on the torsional oscillations of single pile embedded in layered foundation[J].Chinese Journal of Computational Mechanics,2009,26(5):715–721.(in Chinese))
[24]陈刚,蔡袁强,徐长节.双层饱和弹性土中埋置弹性桩的扭转振动[J].哈尔滨工业大学学报,2008,40(12):2029–2034.(CHEN Gang,CAI Yuan-qiang,XU Chang-jie.Torsional vibration of elastic pile embedded in a two-layer poroelastic medium[J].Journal of Harbin Institute of Technology,2008,40(12):2029–2034.(in Chinese))
[25]李强,王奎华,谢康和.饱和土桩纵向振动引起土层复阻抗分析研究[J].岩土工程学报,2004,26(5):679–683.(LI Qiang,WANG Kui-hua,XIE Kang-he.Study on resistance factor of saturated soil caused by longitudinal vibration of pile[J].Chinese Journal of Geotechnical Engineering,2004,26(5):679–683.(in Chinese))
[26]李强,郑辉,王奎华.饱和土中摩擦桩竖向振动解析解及应用[J].工程力学,2011,28(1):157–170.(LI Qiang,ZHENG Hui,WANG Kui-hua.Analytical solution and its application of vertical vibration of a friction pile in saturated soil[J].Engineering Mechanics,2011,28(1):157–170.(in Chinese))
[27]王桂敏,李强,王奎华.单层饱和土中桩竖向振动简化模型及其解析解[J].岩石力学与工程学报,2006,25(2):4233–4240.(WANG Gui-min,LI Qiang,WANG Kui-hua.Simplified model for vertical vibration of pile in single-layer saturated soil and its analytical solution[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(2):4233–4240.(in Chinese))
[28]丁伯阳,童晓刚,陈军,等.排水状态下饱和土中基桩动力特性分析[J].岩土工程学报,2013,35(1):85–95.(DING Bo-yang,TONG Xiao-gang,CHEN Jun,et al.Dynamic properties of a single pile in saturated soil under drainage[J].Chinese Journal of Geotechnical Engineering,2013,35(1):85–95.(in Chinese))
[29]靳建明,张智卿,王奎华,等.任意形式荷载作用下饱和土中桩的扭转振动特性研究[J].振动与冲击,2010,29(7):50–54.(JIN Jian-ming,ZHANG Zhi-qing,WANG Kui-hua,et al.Dynamic torsional response of a pile embedded in porous-saturated soil under arbitrary transient loading[J].Journal of Vibration and Shock,2010,29(7):50–54.(in Chinese))
[30]程泽海,李强,郑辉,等.桩侧扰动分区饱和土中桩竖向振动特性研究[J].计算力学学报,2011,28(4):553–559.(CHENG Ze-hai,LI Qiang,ZHENG Hui,et al.Vertical vibration of pile in saturated soil considering the disturbed radial zone by pile driving[J].Chinese Journal of Computational Mechanics,2011,28(4):553–559.(in Chinese))
[31]吴文兵.基于虚土桩法的桩土纵向耦合振动理论及应用研究[D].杭州:浙江大学,2012.(WU Wen-bing.Vertical vibration theory of pile-soil system based on fictitious soil pile method and its application[D].Hangzhou:Zhejiang University,2012.(in Chinese))
[32]王宁.改进的虚土桩法及其在非等截面桩纵向振动中的应用研究[D].杭州:浙江大学,2013.(WANG Ning.Investigation of improved fictitious soil pile method and its application in longitudinal vibration problems of piles with nonconstant cross sections[D].Hangzhou:Zhejiang University,2013.(in Chinese))
[33]胡秀青.饱和地基中埋置基础的动力振动特性研究[D].杭州:浙江大学,2009.(HU Xiu-qing.Study on the dynamic vibrations of embedded foundation in poroelastic soil[D].Hangzhou:Zhejiang University,2009.(in Chinese))
[34]EDELMAN I,WILMANSKI K.Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces[J].Continuum Mechanics and Thermodynamics,2002,14:25–44.
[35]BOER D R.Contemporary progress in porous media theory[J].Applied Mechanics Reviews,2000,53(12):323–370.
[36]BOER D R.Compressible and incompressible porous media-a new approach[R].GH Essen:Report MECH92/1,FB10/Mechanik,University at-GH Essen,1992.
[37]BOER D R.Highlights in the historical development of the porous media theory:toward a consistent macroscopic theory[J].Applied Mechanics Reviews,1996,49(4):201–262.
[38]BOER D R,EHLERS W.Uplift,friction and capillarity-three fundamental effects for liquid-saturated porous solids[J].International Journal of Solids and Structures,1990,26:43–57.
[39]BOER D R,EHLERS W,LIU Z F.One-dimensional transient wave propagation in fluid saturated porous media[J].Archive of Applied Mechanics,1993,63(1):59–72.
[40]BOER D R,LIU Z F.Plane waves in a semi-infinite fluid saturated porous medium[J].Transport in Porous Media,1994,16(2):147–173.
[41]BOER D R,LIU Z F.Propagation of acceleration waves in incompressible liquid-saturated porous solids[J].Transport in Porous Media,1996,21(2):163–173.
[42]BOER D R,LIU Z F.Growth and decay of acceleration waves in incompressible saturated porous elastic solids[J].Journal of Applied Mathematics and Mechanics,1996,76(6):341–347.
[43]刘占芳,李德源,严波.饱和多孔介质中的非均匀平面波[J].岩土力学,1999,20(4):31–35.(LIU Zhan-fang,LI De-yuan,YAN Bo.Inhomogeneous plane waves in a saturated porous medium[J].Rock and Soil Mechanics,1999,20(4):31–35.(in Chinese))
[44]杨骁,车京兰.饱和黏弹性多孔介质中的平面波及能量耗散[J].力学学报,2005,37(5):579–585.(YANG Xiao,CHE Jing-lan.Plane waves and their energy dissipations in a saturated viscoelastic porous medium[J].Chinese Journal of Theoretical and Applied Mechanics,2005,37(5):579–585.(in Chinese))
[45]张燕,杨骁.不可压饱和黏弹性多孔介质中的Rayleigh波[J].上海大学学报,2007,13(1):62–67.(ZHANG Yan,YANG Xiao.Rayleigh wave in an incompressible saturated viscoelastic porous medium[J].Journal of Shanghai University,2007,13(1):62–67.(in Chinese))
[46]郑云英,杨骁.流体饱和标准线性黏弹性多孔介质中的平面波[J].固体力学学报,2005,26(2):203–206.(ZHENG Yun-ying,YANG Xiao.Plane waves in liquid-saturated viscoelastic porous medium[J].Acta Mechanica Solida Sinica,2005,26(2):203–206.(in Chinese))
[47]NOVAK M,BEREDUGO Y.Vertical vibration of embedded footings[J].Journal of the Soil Mechanics and Foundations Division,1972,98(12):1291–1310.
[48]BARANOV V A.On the calculation of excited vibrations of an embedded foundation(in Russian)[J].Polytechnical Institute of Riga:Voprosy Dynamiki:Prochnocti,1967,14(5):195–207.
[49]SNEDDON,IAN H.The use of integral transforms[M].New York:Mc Graw-Hill Book Company,1972.
[50]TRANTER C J.On some dual integral equations occurring in potential problems with axial symmetry[J].Quartly Journal of Mechanics and Applied Mathematics,1950,3:411–419.
[51]NOBEL B.The solution of Bessel-function dual integral equations by a multiplying-factor method[J].Mathematical Proceedings of the Cambridge Philosophical Society,1963,59:351–362.
[52]李强,王奎华.饱和土中桩竖向耦合振动理论与应用[M].北京:中国水利水电出版社,2010:1–147.(LI Qiang,WANG Kui-hua.The theory on vertical coupled vibration of pile in saturated soil and its application[M].Beijing:China Water Power Press,2010:1–147.(in Chinese))
[53]SENJUNTICHAI T,RAJAPAKSE R K N D.Transient response of a circular cavity in a poroelastic medium[J].International Journal for Numerical and Analytical Methods in Geomechanics,1993,17:357–383.
[2]LU J F,JENG D S,NIE W D.Dynamic response of a pile embedded in a porous medium subjected to plane SH waves[J].Computers and Geotechnics,2006,33:404–418.
[3]CHEN G,CAI Y Q,LIU F Y,et al.Dynamic response of a pile in a transversely isotropic saturated soil to transient tensional loading[J].Computers and Geotechnics,2007,34(8):1–5.
[4]陆建飞.频域内半空间饱和土中水平受荷桩的动力分析[J].岩石力学与工程学报,2002,21(4):577–581.(LU Jian-fei.Dynamic frequency domain analysis on laterally loaded pile in saturated soil[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(4):577–581.(in Chinese))
[5]陆建飞,聂卫东.饱和土中单桩在瑞利波作用下的动力响应[J].岩土工程学报,2008,30(2):225–231.(LU Jian-fei,NIE Wei-dong.Dynamic response of single pile embedded in half-space saturated soil subjected to Rayleigh waves[J].Chinese Journal of Geotechnical Engineering,2008,30(2):225–231.(in Chinese))
[6]杨军,宋二祥,陈肇元.桩在饱和土中水平振动的辐射阻尼简化算法[J].岩土力学,2002,23(2):179–183.(YANG Jun,SONG Er-xiang,CHEN Zhao-yuan.Simple radiation damping model for horizontally vibrating pile in saturated soil[J].Rock and Soil Mechanics,2002,23(2):179–183.(in Chinese))
[7]张智卿,王奎华,谢康和.饱和土层中桩的扭转振动响应分析[J].浙江大学学报,2006,40(7):1211–1218.(ZHANG Zhi-qing,WANG Kui-hua,XIE Kang-he.Study on torsional vibration of pile embedded in saturated soil[J].Journal of Zhejiang University,2006,40(7):1211–1218.(in Chinese))
[8]李强,王奎华,谢康和.饱和土中端承桩纵向振动特性研究[J].力学学报,2004,36(4):435–442.(LI Qiang,WANG Kui-hua,XIE Kang-he.Vertical vibration of an end bearing pile embedded in saturated soil[J].Acta Mechanica Sinica,2004,36(4):435–442.(in Chinese))
[9]李强,王奎华,谢康和.饱和土中大直径嵌岩桩纵向振动特性研究[J].振动工程学报,2005,18(4):500–505.(LI Qiang,WANG Kui-hua,XIE Kang-he.Dynamic response for vertical vibration of large diameter pile in saturated soil[J].Journal of Vibration Engineering,2005,18(4):500–505.(in Chinese))
[10]李强.饱和土中端承桩非完全黏结下的竖向振动特性[J].水利学报,2007,38(3):349–354.(LI Qiang.Vertical vibration of piles embedded in saturated soil considering the imperfect contact[J].Journal of Hydraulic Engineering,2007,38(3):349–354.(in Chinese))
[11]尚守平,余俊,王海东,等.饱和土中桩水平振动分析[J].岩土工程学报,2007,29(11):1696–1702.(SHANG Shou-ping,YU Jun,WANG Hai-dong,et al.Horizontal vibration of piles in saturated soil[J].Chinese Journal of Geotechnical Engineering,2007,29(11):1696–1702.(in Chinese))
[12]刘林超,杨骁.基于多孔介质理论的饱和土-桩纵向耦合振动研究[J].土木工程学报,2009,42(9):89–95.(LIU Lin-chao,YANG Xiao.Study of vertical coupled vibrations of piles in saturated soils using porous medium theory[J].China Civil Engineering Journal,2009,42(9):89–95.(in Chinese))
[13]刘林超,苏子平.层状饱和土中单桩纵向振动分析[J].公路交通科技,2010,27(12):5–9.(LIU Lin-chao,SU Zi-ping.Analysis of vertical vibration of single pile in layered saturated soil[J].Journal of Highway and Transportation Research and Development,2010,27(12):5–9.(in Chinese))
[14]刘林超,闫启方.饱和土中管桩的纵向振动特性[J].水力学报,2011,42(3):366–378.(LIU Lin-chao,YAN Qi-fang.Vertical vibration characteristics of pipe pile in saturated soil[J].Journal of Hydraulic Engineering,2011,42(3):366–378.(in Chinese))
[15]杨骁,唐洁.成层饱和土中考虑横向惯性的单桩纵向振动[J].岩土力学,2013,34(6):1560–1566.(YANG Xiao,TANG Jie.Vertical vibration of single pile with transversal inertia effect in stratified saturated soil[J].Rock and Soil Mechanics,2013,34(6):1560–1566.(in Chinese))
[16]杨骁,刘慧,蔡雪琼.端承黏弹性桩纵向振动的轴对称解析解[J].固体力学学报,2012,33(4):423–430.(YANG Xiao,LIU Hui,CAI Xue-qiong.Axisymmetrical analytical solution for vertical vibration of end-bearing viscoelastic pile[J].Chinese Journal of Solid Mechanics,2012,33(4):423–430.(in Chinese))
[17]杨骁,蔡雪琼.考虑横向效应饱和黏弹性土层中桩的纵向振动[J].岩土力学,2011,32(6):1857–1863.(YANG Xiao,CAI Xue-qiong.Vertical vibration of pile in saturated viscoelastic soil layer considering transversal effects[J].Rock and Soil Mechanics,2011,32(6):1857–1863.(in Chinese))
[18]王小岗.横观各向同性饱和土中柱面载荷的动力Green函数[J].力学学报,2010,42(5):909–918.(WANG Xiao-gang.Dynamic Green’s function for internal barrel loads in transversely isotropic saturated soils[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(5):909–918.(in Chinese))
[19]闫启方,刘林超.基于多孔介质理论的饱和土中单桩的扭转复刚度研究[J].岩土工程学报,2010,32(9):1460–1463.(YAN Qi-fang,LIU Lin-chao.Torsional complex stiffness of single pile in saturated soil based on theory of porous medium[J].Chinese Journal of Geotechnical Engineering,2010,32(9):1460–1463.(in Chinese))
[20]闫启方,刘林超.考虑波动效应的SH简谐地震波作用下单桩水平振动研究[J].岩土工程学报,2012,34(8):1483–1487.(YAN Qi-fang,LIU Lin-chao.Lateral vibration of a single pile under SH harmonic seismic waves considering three-dimensional wave effect[J].Chinese Journal of Geotechnical Engineering,2012,34(8):1483–1487.(in Chinese))
[21]秦世伟,莫泷,史蕙质.轴力作用下液化土中端承桩的水平振动特性[J].岩土力学,2013,34(4):987–995.(QIN Shi-wei,MO Long,SHI Hui-zhi.Characteristics of horizontal vibration of end-bearing piles in liquefied soils under axial force[J].Rock and Soil Mechanics,2013,34(4):987–995.(in Chinese))
[22]王建华,陆建飞,王卫东,等.移动荷载作用下饱和土中单桩的动力响应[J].岩土力学,2007,28:693–697.(WANG Jian-hua,LU Jian-fei,WANG Wei-dong,et al.Dynamic response of a single pile embedded in a poroelastic soil to moving loads[J].Rock and Soil Mechanics,2007,28:693–697.(in Chinese))
[23]王国才,丁翠红,王哲,等.层状地基中单桩扭转振动特性分析[J].计算力学学报,2009,26(5):715–721.(WANG Guo-cai,DING Cui-hong,WANG Zhe,et al.Study on the torsional oscillations of single pile embedded in layered foundation[J].Chinese Journal of Computational Mechanics,2009,26(5):715–721.(in Chinese))
[24]陈刚,蔡袁强,徐长节.双层饱和弹性土中埋置弹性桩的扭转振动[J].哈尔滨工业大学学报,2008,40(12):2029–2034.(CHEN Gang,CAI Yuan-qiang,XU Chang-jie.Torsional vibration of elastic pile embedded in a two-layer poroelastic medium[J].Journal of Harbin Institute of Technology,2008,40(12):2029–2034.(in Chinese))
[25]李强,王奎华,谢康和.饱和土桩纵向振动引起土层复阻抗分析研究[J].岩土工程学报,2004,26(5):679–683.(LI Qiang,WANG Kui-hua,XIE Kang-he.Study on resistance factor of saturated soil caused by longitudinal vibration of pile[J].Chinese Journal of Geotechnical Engineering,2004,26(5):679–683.(in Chinese))
[26]李强,郑辉,王奎华.饱和土中摩擦桩竖向振动解析解及应用[J].工程力学,2011,28(1):157–170.(LI Qiang,ZHENG Hui,WANG Kui-hua.Analytical solution and its application of vertical vibration of a friction pile in saturated soil[J].Engineering Mechanics,2011,28(1):157–170.(in Chinese))
[27]王桂敏,李强,王奎华.单层饱和土中桩竖向振动简化模型及其解析解[J].岩石力学与工程学报,2006,25(2):4233–4240.(WANG Gui-min,LI Qiang,WANG Kui-hua.Simplified model for vertical vibration of pile in single-layer saturated soil and its analytical solution[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(2):4233–4240.(in Chinese))
[28]丁伯阳,童晓刚,陈军,等.排水状态下饱和土中基桩动力特性分析[J].岩土工程学报,2013,35(1):85–95.(DING Bo-yang,TONG Xiao-gang,CHEN Jun,et al.Dynamic properties of a single pile in saturated soil under drainage[J].Chinese Journal of Geotechnical Engineering,2013,35(1):85–95.(in Chinese))
[29]靳建明,张智卿,王奎华,等.任意形式荷载作用下饱和土中桩的扭转振动特性研究[J].振动与冲击,2010,29(7):50–54.(JIN Jian-ming,ZHANG Zhi-qing,WANG Kui-hua,et al.Dynamic torsional response of a pile embedded in porous-saturated soil under arbitrary transient loading[J].Journal of Vibration and Shock,2010,29(7):50–54.(in Chinese))
[30]程泽海,李强,郑辉,等.桩侧扰动分区饱和土中桩竖向振动特性研究[J].计算力学学报,2011,28(4):553–559.(CHENG Ze-hai,LI Qiang,ZHENG Hui,et al.Vertical vibration of pile in saturated soil considering the disturbed radial zone by pile driving[J].Chinese Journal of Computational Mechanics,2011,28(4):553–559.(in Chinese))
[31]吴文兵.基于虚土桩法的桩土纵向耦合振动理论及应用研究[D].杭州:浙江大学,2012.(WU Wen-bing.Vertical vibration theory of pile-soil system based on fictitious soil pile method and its application[D].Hangzhou:Zhejiang University,2012.(in Chinese))
[32]王宁.改进的虚土桩法及其在非等截面桩纵向振动中的应用研究[D].杭州:浙江大学,2013.(WANG Ning.Investigation of improved fictitious soil pile method and its application in longitudinal vibration problems of piles with nonconstant cross sections[D].Hangzhou:Zhejiang University,2013.(in Chinese))
[33]胡秀青.饱和地基中埋置基础的动力振动特性研究[D].杭州:浙江大学,2009.(HU Xiu-qing.Study on the dynamic vibrations of embedded foundation in poroelastic soil[D].Hangzhou:Zhejiang University,2009.(in Chinese))
[34]EDELMAN I,WILMANSKI K.Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces[J].Continuum Mechanics and Thermodynamics,2002,14:25–44.
[35]BOER D R.Contemporary progress in porous media theory[J].Applied Mechanics Reviews,2000,53(12):323–370.
[36]BOER D R.Compressible and incompressible porous media-a new approach[R].GH Essen:Report MECH92/1,FB10/Mechanik,University at-GH Essen,1992.
[37]BOER D R.Highlights in the historical development of the porous media theory:toward a consistent macroscopic theory[J].Applied Mechanics Reviews,1996,49(4):201–262.
[38]BOER D R,EHLERS W.Uplift,friction and capillarity-three fundamental effects for liquid-saturated porous solids[J].International Journal of Solids and Structures,1990,26:43–57.
[39]BOER D R,EHLERS W,LIU Z F.One-dimensional transient wave propagation in fluid saturated porous media[J].Archive of Applied Mechanics,1993,63(1):59–72.
[40]BOER D R,LIU Z F.Plane waves in a semi-infinite fluid saturated porous medium[J].Transport in Porous Media,1994,16(2):147–173.
[41]BOER D R,LIU Z F.Propagation of acceleration waves in incompressible liquid-saturated porous solids[J].Transport in Porous Media,1996,21(2):163–173.
[42]BOER D R,LIU Z F.Growth and decay of acceleration waves in incompressible saturated porous elastic solids[J].Journal of Applied Mathematics and Mechanics,1996,76(6):341–347.
[43]刘占芳,李德源,严波.饱和多孔介质中的非均匀平面波[J].岩土力学,1999,20(4):31–35.(LIU Zhan-fang,LI De-yuan,YAN Bo.Inhomogeneous plane waves in a saturated porous medium[J].Rock and Soil Mechanics,1999,20(4):31–35.(in Chinese))
[44]杨骁,车京兰.饱和黏弹性多孔介质中的平面波及能量耗散[J].力学学报,2005,37(5):579–585.(YANG Xiao,CHE Jing-lan.Plane waves and their energy dissipations in a saturated viscoelastic porous medium[J].Chinese Journal of Theoretical and Applied Mechanics,2005,37(5):579–585.(in Chinese))
[45]张燕,杨骁.不可压饱和黏弹性多孔介质中的Rayleigh波[J].上海大学学报,2007,13(1):62–67.(ZHANG Yan,YANG Xiao.Rayleigh wave in an incompressible saturated viscoelastic porous medium[J].Journal of Shanghai University,2007,13(1):62–67.(in Chinese))
[46]郑云英,杨骁.流体饱和标准线性黏弹性多孔介质中的平面波[J].固体力学学报,2005,26(2):203–206.(ZHENG Yun-ying,YANG Xiao.Plane waves in liquid-saturated viscoelastic porous medium[J].Acta Mechanica Solida Sinica,2005,26(2):203–206.(in Chinese))
[47]NOVAK M,BEREDUGO Y.Vertical vibration of embedded footings[J].Journal of the Soil Mechanics and Foundations Division,1972,98(12):1291–1310.
[48]BARANOV V A.On the calculation of excited vibrations of an embedded foundation(in Russian)[J].Polytechnical Institute of Riga:Voprosy Dynamiki:Prochnocti,1967,14(5):195–207.
[49]SNEDDON,IAN H.The use of integral transforms[M].New York:Mc Graw-Hill Book Company,1972.
[50]TRANTER C J.On some dual integral equations occurring in potential problems with axial symmetry[J].Quartly Journal of Mechanics and Applied Mathematics,1950,3:411–419.
[51]NOBEL B.The solution of Bessel-function dual integral equations by a multiplying-factor method[J].Mathematical Proceedings of the Cambridge Philosophical Society,1963,59:351–362.
[52]李强,王奎华.饱和土中桩竖向耦合振动理论与应用[M].北京:中国水利水电出版社,2010:1–147.(LI Qiang,WANG Kui-hua.The theory on vertical coupled vibration of pile in saturated soil and its application[M].Beijing:China Water Power Press,2010:1–147.(in Chinese))
[53]SENJUNTICHAI T,RAJAPAKSE R K N D.Transient response of a circular cavity in a poroelastic medium[J].International Journal for Numerical and Analytical Methods in Geomechanics,1993,17:357–383.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心