横观各向同性层状饱和土动力问题的反射、透射矩阵方法  

Reflection-transmission matrix method for dynamic response of transversely isotropic multilayered saturated soil

作　　者：陆建飞[1] 周慧明 刘洋 LU Jian-fei;ZHOU Hui-ming;LIU Yang(Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, Jiangsu 212013, China)

机构地区：[1]江苏大学土木工程与力学学院,江苏镇江212013

出　　处：《岩土力学》2018年第6期2219-2226,共8页Rock and Soil Mechanics

基　　金：国家自然科学基金(No.11272137)~~

摘　　要：建立了轴对称情形下横观各向同性层状饱和土(TISS)动力问题的反射、透射矩阵(RTM)方法。对横观各向同性饱和土状态向量所满足的偏微分方程组进行Fourier和Hankel变换,得到状态向量所满足的常微分方程组。求解该常微分方程组,得到横观各向同性饱和土状态向量的通解。根据该通解得出了状态向量和波向量的传递矩阵,由波向量的传递矩阵得出了层状土的反射、透射矩阵表达式。利用上述反射、透射矩阵,并结合层状饱和土的边界条件和层间连续性条件,得出了垂直力作用下横观各向同性层状饱和土在变换域内的解。对变换域内的解进行Hankel逆变换,得出了频域内层状饱和土的动力响应。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.

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 

分 类 号：TU435[建筑科学—岩土工程]