3D横观各向同性地基非耦合解析层元

Uncoupled analytical layer-element for 3D transversely isotropic multilayered foundation

基于Fourier变换域内直角坐标系下3D横观各向同性单层地基的控制方程,借助于降阶法,推导出单层地基非耦合的精确刚度矩阵即解析层元,然后根据有限层法原理并引入相应的边界条件,组装并求解总体刚度矩阵,最后通过Fourier逆变换技术获得物理域内的真实解答。编制了相应的Fortran程序进行数值计算,并与ABAQUS模拟结果进行对比以验证本文方法及结果的正确性,计算分析结果表明:地基的横观各向同性特性与成层特性对地基的沉降有较大的影响。

Based on the governing equations in Fourier transform domain for 3D transversely isotropic single-layer foundation in Cartesian coordinate system, and applying the order reduction method, an uncoupled exact stiffness matrix, i.e., the analytical layer-element of single-layer foundation, is obtained. Following the principle of the finite layer method, and introducing the corresponding boundary conditions, the total stiffness matrix is assembled and solved. In order to verify the proposed method, numerical results are obtained by the compiled procedure and compared with those by ABAQUS, which shows a good agreement. Other results demonstrate that the transversely isotropic and multilayered properties of the foundation have a great impact on its vertical displacements.