饱和层状地基的瞬态动力响应分析
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摘要
在Biot饱和多孔介质理论的基础上,应用Laplace变换、Fourier级数展开和Hankel变换将波动方程转化为一组二阶常微分方程;运用薄层法原理在竖向进行离散求解,得到饱和层状地基Lamb问题的Laplace域内解答,并利用Laplace数值逆变换最终得到时域内的数值解答,最后,通过计算实例验证了本文方法.
The transient response of saturated layered ground subjected to concentrated loads is investigated.By using Laplace transform,Fourier series expansion and Hankel transform,the Biot's dynamic equations in each layer are reduced into a series of ordinary differential equations,which can be solved by thin layered method(TLM).The general solutions for displacement and pore pressure in Laplace domain are derived by analytical inversion of Hankel transform,and the solutions in time domain are obtained by numerical inverison of Laplace transform.Finally,some examples are given to validate the method.
The transient response of saturated layered ground subjected to concentrated loads is investigated.By using Laplace transform,Fourier series expansion and Hankel transform,the Biot's dynamic equations in each layer are reduced into a series of ordinary differential equations,which can be solved by thin layered method(TLM).The general solutions for displacement and pore pressure in Laplace domain are derived by analytical inversion of Hankel transform,and the solutions in time domain are obtained by numerical inverison of Laplace transform.Finally,some examples are given to validate the method.
引文
[1]BOITM A.Theory of propagation of elastic waves in afluid-saturated porous solid(I)Low-frequencyrange[J].J Acoust Soc Am,1956,28:168-78.
[2]PHILIPPACOPOULOS A J.Lamb’s problem for fluid-saturated porous media[J].Bull seism Soc Am,1988,78(2):908-923.
[3]王立忠,陈云敏,吴世明,等.饱和弹性半空间在低频谐和集中力下的积分形式解[J].水利学报,1996(2):84-89.
[4]LU J F,WANG J H,SHEN W P.The green’s func-tion of the harmonic horizontal force applied at the in-terior of the saturated half-space soil[J].Acta Seis-mologica Sinica,2001,14(2):196-202.
[5]陈胜立,张建民,陈龙珠.饱和土埋置力源的三维动力Lamb问题解答[J].固体力学学报,2004,25(2):149-154.
[6]黄义,张玉红.饱和土三维非轴对称Lamb问题[J].中国科学:E辑,2000,30(4):375-384.
[7]张引科,黄义.弹性饱和多孔介质在非轴对称荷载下的稳态动力响应[J].土木工程学报,2002,35(3):41-45.
[8]蔡袁强,徐长节,郑灶峰,等.轴对称饱和地基竖向振动分析[J].应用数学与力学,2006,27(1):75-80.
[9]张玉红,黄义,王忠建.层状饱水软土地基三维非轴对称动力响应分析方法[J].地震工程与工程振动,2002,22(4):47-52.
[10]周香莲,王建华,陆建飞.半空间饱和土作用垂直集中荷载时的瞬态解[J].上海交通大学学报,2002,36(3):428-431.
[11]时刚.饱和地基中Rayleigh波的传播与屏障隔振研究[D].上海:同济大学土木工程学院,2008.
[12]CHAO C C.Dynamical vesporise of an elastic half-space to tangertial surface logcling[J].Journal of Ap-plied Mechanics,1960,27:559-567.
[2]PHILIPPACOPOULOS A J.Lamb’s problem for fluid-saturated porous media[J].Bull seism Soc Am,1988,78(2):908-923.
[3]王立忠,陈云敏,吴世明,等.饱和弹性半空间在低频谐和集中力下的积分形式解[J].水利学报,1996(2):84-89.
[4]LU J F,WANG J H,SHEN W P.The green’s func-tion of the harmonic horizontal force applied at the in-terior of the saturated half-space soil[J].Acta Seis-mologica Sinica,2001,14(2):196-202.
[5]陈胜立,张建民,陈龙珠.饱和土埋置力源的三维动力Lamb问题解答[J].固体力学学报,2004,25(2):149-154.
[6]黄义,张玉红.饱和土三维非轴对称Lamb问题[J].中国科学:E辑,2000,30(4):375-384.
[7]张引科,黄义.弹性饱和多孔介质在非轴对称荷载下的稳态动力响应[J].土木工程学报,2002,35(3):41-45.
[8]蔡袁强,徐长节,郑灶峰,等.轴对称饱和地基竖向振动分析[J].应用数学与力学,2006,27(1):75-80.
[9]张玉红,黄义,王忠建.层状饱水软土地基三维非轴对称动力响应分析方法[J].地震工程与工程振动,2002,22(4):47-52.
[10]周香莲,王建华,陆建飞.半空间饱和土作用垂直集中荷载时的瞬态解[J].上海交通大学学报,2002,36(3):428-431.
[11]时刚.饱和地基中Rayleigh波的传播与屏障隔振研究[D].上海:同济大学土木工程学院,2008.
[12]CHAO C C.Dynamical vesporise of an elastic half-space to tangertial surface logcling[J].Journal of Ap-plied Mechanics,1960,27:559-567.
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