关键词: 层状横观各向同性饱和土, Fourier变换, Hankel变换, 反射、透射矩阵, 动力响应

Abstract: Reflection-transmission matrix method for the dynamic response of the layered transversely isotropic saturated soil (TISS) under axisymmetric deformation is established in this study. Applied the Fourier and Hankel transforms, the partial differential equations satisfied by the state vector of the TISS can be duduced to the corresponding ordinary differential equations for the state vector. Solving the ordinary differential equations yields the general solutions for the state vector of the TISS. Based on the aforementioned general solutions, the transfer matrices of the state vector and wave vector are obtained. Reflection-transmission matrices of the layered TISS are derived by the transfer matrix of the wave vector. By using the obtained reflection-transmission matrices, the boundary conditions and the continuity conditions at the interfaces of the soil layers, the transformed domain solution of the layered TISS subjected to a vertical force is obtained. Applying the inverse Hankel transform to the transformed domain solution of the TISS gives the frequency domain response of the TISS.

Key words: layered transversely isotropic saturated soil (TISS), Fourier transform, Hankel transform, reflection-transmission matrix, dynamic response