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研究了横观各向同性饱和土地基在地表动力荷载作用下的三维瞬态响应。基于饱和多孔介质的三维Biot波动理论,利用Laplace变换,建立圆柱坐标系下横观各向同性饱和土的波动方程;解耦波动方程后,根据算子理论,并借助Fourier展开和Hankel变换技术,得到瞬态荷载作用下,饱和土介质的土骨架位移和应力、孔隙水相对位移和孔隙水压力的一般解;利用一般解,给出横观各向同性饱和地基在地表集中荷载激励下的瞬态Lamb问题的解答。数值算例结果表明,采用各向同性饱和介质的动力学模型,不能准确描述具有明显各向异性特性的饱和土地基的瞬态动力特性。
The three-dimensional transient response of a transversely isotropic saturated soil subjected to surface dynamic loads is studied. Based on the three-dimensional Biot wave theory of saturated porous media, the wave equation of transversely isotropic saturated soil in cylindrical coordinate system is established by Laplace transform. After the decoupled wave equation, based on operator theory and Fourier expansion and Hankel transform, The general solution to the displacement and stress of soil skeleton, the relative displacement of pore water and the pore water pressure under transient load are obtained. By means of the general solution, the moment of transversely isotropic saturated soil under the concentrated surface load excitation is obtained. Lamb answer the question. The numerical results show that the dynamic model of isotropic saturated medium can not accurately describe the transient dynamic characteristics of saturated soil foundation with obvious anisotropy.