3-D Dynamic Response of Transversely Isotropic Saturated Soils
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摘要: 首先引入位移函数，将直角坐标系下横观各向同性饱和土Biot波动方程转化为2个解耦的六阶和二阶控制方程；然后基于双重Fourier变换，求解了Biot波动方程，得到以土骨架位移和孔隙水压力为基本未知量的积分形式的一般解，并用一般解给出了饱和土总应力分量的表达式．在此基础上系统研究了横观各向同性饱和半空间体的稳态动力响应问题，考虑表面排水和不排水两种情况，得到了半空间体在任意分布的表面谐振荷载作用下，表面位移的稳态动力响应，文末给出了算例．
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关键词:
- 横观各向同性饱和土 /
- Biot波动方程 /
- 动力响应 /
- 双重Fourier变换
Abstract: A study on dynamic response of transversely isotropic saturated poroelastic media under a circular non-axisymmetica harmonic source has been presented by HUANG Yi et al.using the technique of Fourier expansion and Hankel transform.However,the method may not always be valid.The work is extended to the general case being in the rectangular coordinate.The purpose is to study the 3-d dynamic response of transversely isotropic saturated soils under a general source distributing in arbitrary rectangular zoon on the medium surface.Based on Biot's theory for fluid-saturated porous media,the 3-d wave motion equations in rectangular coordinate for transversely isotropic saturated poroelastic media were transformed into the two uncoupling governing differential equations of 6-order and 2-order respectively by means of the displacement functions.Then,using the technique of double Fourier transform,the governing differential equations were easily solved.Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media were obtained.Furthermore,a systematic study on half-space problem in saturated soils was performed.Integral solutions for surface displacements under the general harmonic source distributing on arbitrary surface zone,considering both case of drained surface and undrained surface,were presented. -
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